Let me try a summary how analog CRT monitors work(ed).
Let's start with monochrome, later explain the color models, and then answer your questions.
How it works
The CRT produces a thin electron beam that produces light when it hits the phosphor. A deflection circuitry can bend that beam so that it can reach all of the sreen front area. This circuitry is driven by two ramp signals:
- A low-frequency signal (e.g. 50Hz) for the vertical direction, so the beam starts at the top of the screen and continuously moves downward to the end, then quickly returns to the top, all this e.g. within 20ms.
- A higher-frequency signal (e.g. 25kHz) for the horizontal direction, moving the beam from left to right, and then quickly returning (within e.g. 40µs).
Combining both circuits, the beam moves along a raster pattern of nearly horizontal lines covering the screen front.
The video card provides:
- a clock signal (called VSYNC) telling the monitor when to vertically return ("retrace") to the top position,
- a clock signal (called HSYNC) telling the monitor when to horizontally return to the left position,
- an intensity signal commanding the current beam intensity to the monitor.
The deflection circuitry can only work within some given frequency ranges, so the video card isn't completely free to decide on these frequencies, but must create a timing appropriate for the monitor.
The intensity signal is zero during the times when the monitor is expected to do the horizontal or the vertical beam return.
So, the intensity signal is active (non-zero) during the major part of one horizontal cycle, e.g. during 32 of the 40µs. This time corresponds to the srceen width (the beam moves across the screen from left to right during that time), and the video card divides this time into slots corresponding to horizontal pixels, e.g. to fit 640 pixels into 32µs, each pixel occupies 0.05µs. In each of these pixel slots, the video card provides an intensity voltage corresponding to the desired screen brightness of that pixel.
Resolution
So, what's the resolution we get?
The vertical resolution is given by counting the horizontal cycles that fit into one vertical cycle, being the ratio between horizontal and vertical sync frequencies (minus the time for vertical retrace), e.g. 25kHz / 50Hz = 500, meaning that maybe 450 lines are usable.
So, the vertical resolution is given by the video card. But, as the acceptable sync frequencies are constrained by the monitor, the card isn't completely free in its decision.
The horizontal resolution also is defined by the video signal, by the aspect, how many different analog intensity values the card emits during one horizontal line. Here, the video card is completely free to produce whatever number of pixels it wants, but the monitor's beam controlling amplifier has its limits, so it won't be able to follow the signal changes exactly, if they come too fast, resulting in a horizontally blurry impression.
One additional aspect impacts the resolution: the diameter of the electron beam. If the beam size is too large, multiple scan lines overlap, so you can't distinguish the individual values from vertically-adjacent pixels. But the beam can also be "too thin", resulting in unpleasant gaps between the horizontal lines. And of course, large beam diameters also amount to horizontal blurriness. So, sending a high-resolution signal to a monitor with a blurry beam might be technically possible, but won't give the desired crisp image.
One remark on pixel aspect ratio:
As horizontal and vertical resolution are controlled by completely different timing aspects, it's easy to get pixels that aren't square, meaning different horizontal and vertical dpi values, resulting e.g. in circles appearing as ellipses.
Linearity
As the picture geometry is mainly controlled by the beam deflection circuitry, it's important that the beam moves with constant speed (at least during the active signal periods). Otherwise, you'd get different pixel scales over the screen size, resulting in distortions. CRTs never achieved perfect linearity, but many of them could fine-tune various aspects of that deflection, e.g.
- Horizontal size: this modifies the amplification of the horizontal-deflection circuitry, making the beam cover a wider horizontal range within the given horizontal time.
- Vertical size: this modifies the amplification of the vertical-deflection circuitry, making the beam cover a taller vertical range within the given vertical time.
- Pillow correction: adding correction signals to the deflection system so that the corners get the same deflection ratio as the center (pillow error: there is too much deflection in the corners, barrel error: the center gets more deflection than the corners).
Color CRT
A color CRT works mostly the same, but:
- There are three electron cannons, producing three beams (meant for R, G, and B). Some monitors arrange them in a row, others in a triangle configuration.
- The beams have to go through a mask with holes before hitting the phosphor surface.
- Coming from different electron cannons at different positions, after passing through one hole of the mask, the three beams hit the phosphor surface at different positions.
- At these different positions, phosphors of different color are applied, so the electrons coming from the "R" cannon only hit red phosphor dots, the "G" electrons only green dots, and the "B" ones only blue dots.
- The deflection circuitry deflects all three beams the same way, so they always hit the same spot of the screen front.
- The video card provides three intensity signals, simultaneously controlling the three electron cannons.
With color CRT, we have one more aspect limiting the effective resolution: mask and the dotted phosphor surface need to be finely pitched to allow for the desired resolution. If a single RGB tripel is bigger than the desired pixel size, you don't get the impression of a "single mixed-color dot", but individual red, green, and blue dots.
Your questions
Phosphor resolution only applies to color CRTs, being the dot pitch. Dot pitch has to be clearly smaller than the desired size of a single pixel.
There were both dot-mask and slit-mask monitors. Dot-mask corresponds to a triangle configuration of the cannons, slit-mask to a linear one.
In theory, a dot mask imposes a limit on vertical resolution, but in reality other factors dominated: the beam diameter, and the difficulty of having three beams hit the same screen spot.
As explained above, the video card controlled the resolution by using an appropriate timing, but that had to fit within the limits of the monitor.
The position and size on screen could be controlled by both the video card and the monitor:
- The card could start its intensity signal earlier or later (horizontally as well as vertically), resulting in the image moving left or right (or up and down).
- The card could use more or less of the available beam-moving time, thus producing a bigger or a smaller image.
- The monitor could adjust amplification and possibly offset of the deflection ramp signals, thus magnifying and/or moving the image, both horizontally as well as vertically.
From the video card's point of view, the scan line width was the same over the full screen. There was no reason to generate shorter and longer scan lines. But the analog beam deflection circuitry never was perfectly linear, so it was quite common that the image width varied slightly over the screen height (e.g. cushion or barrel distortion).
The time to draw a scan line was always constant, corresponding to the horizontal sync frequency. Monitors were designed for constant H and V frequencies, and always needed some time to adapt to different ones.
The vertical distance between scan lines was given by the amount of vertical deflection corresponding to one horizontal cycle. E.g. with a 50Hz / 25kHz setting, each scan line consumed 40µs, and within 40µs the vertical deflection advanced by roughly 1/450 of the screen height (not 1/500 to account for the vertical retrace).
The number of scan lines was given by the ratio between horizontal and vertical scan frequencies (minus the time needed for vertical retrace).
A video card could in theory produce any pixel resolution desired. Limiting factors were:
- The maximum pixel clock rate, making e.g. 1000*1000 hard to achieve in this era (60MHz or more necessary).
- The horizontal and vertical scan frequencies that the monitor was capable to handle.
- The unpleasant appearance of low vertical resolution with thin electron beams, resulting in visible gaps between the lines.