A cassette interface only needs to fit a single transmission channel at a time, while a modem needs to hold two.
Cassette tape is made for a different (broader) frequency range than the phone network.
It's all about easy separation of whatever signals are present and suppressing everything else.
Number of Channels
A cassette interface is by definition unidirectional. There is only one transmission at a time from a single sender (*1). Thus only a single pair of signals (frequencies) is needed, which can be spaced equally across the available bandwidth.
A modem needs to hold two channels, each a pair of tones. As a result the phone bandwidth needs to be divided into two equally wide channels, each holding one transmission.
In all practical implementation this will be done by a filter only letting thru whatever half of the bandwidth should be received (*2).
Bandwidth (Frequency Range)
While it is true that a telephone line is defined for a frequency range of roughly 300 to 3400Hz, while a cassette tape is good for 40..12,000 Hz, this is not really an issue, as frequencies for (most) cassette interfaces are kept well below 3000 Hz.
A real world channel isn't a nice box of equal size, but is shaped by filter functions dampening a signal different over the frequency range. As closer it gets to the 'edges', as more a signal is lowered. In reverse this means the best transmission (recording) is right at the middle (*3). So the least dampened (aka best) signal frequency for a phone line is about 1000 Hz to 2700 Hz. Let, for simplicity, assume the same for a cassette recording (*4).
Third: Signal Separation
Next, not all frequencies are present at the same time.
A modem holds two channels, Originate and Answer, each can transmit one of two signals, Mark and Space, at a given time. Thus at maximum two frequencies are present at a given time. This table shows the resulting nine combinations:
Case Originate Answer
1 None None
2 None Mark
3 None Space
4 Mark None
5 Mark Mark
6 Mark Space
7 Space None
8 Space Mark
9 Space Space
So the goal is to make each of these nine states recognizeable with the least doubt possible. It's easy if no signal or only one signal is present. for all other cases, we want to have the two signals as far apart as possible while itself being apart from cut off. So let's enter the Bell 103 frequencies to see how they did it:
(Assuming the 300..3400 Range)
Case Originate Answer Separation
1 - - -
2 - 2025 1325/1375
3 - 2225 1525/1175
4 1070 - 770/2330
5 1070 2025 770/ 955/1375
6 1070 2225 770/1155/1175
7 1270 - 970/2130
8 1270 2025 970/ 755/1375
9 1270 2225 970/ 955/1175
We see that at any given time any signal has is at least 700 Hz from any channel cut off, as well at least 700 Hz from each other. This will quite good satisfy the need of least dampening while at the same time maximum separation. Great for good detection, isn't it?
For a cassette recording things are way less complicated. There is only one sender active at any given time and it can use the whole spectrum, assuming again 300..3400 Hz, 1330 Hz and 2370 Hz would make a great pair.
Making it 1200 and 2400, as chosen by CUTS, is not only close, but as well easy to remember and implement.
Long story short: Same transmission channel but different use case.
Similar examples also find differences in frequencies, like Bell 103/V.21, Bell 212/V.22.
Nop, they are not due the same fact, as between modem and cassette, but regarding different bandwidth available. ITU standards are meant to operate across different networks. Some countries use(d) smaller phone channels with an upper end below 3000 Hz, to keep equal distance to cut of filters, frequencies had to be closer. That's why all ITU frequencies are lower than BELL frequencies for the same purpose. On the other hand, signal distance was kept the same to enable multi standard modems
*1 - Handover between sending (writing) and receiving (reading) is done by rewinding and listening to a different pair of lines :))
*2 - Originate frequencies by the station called, Answer frequencies by the station calling.
*3 - Well, not really true, especially not for recording devices as their filter function is based around an off middle peak, but for this issue we simply go by middle point.
*4 - As the makers of CUTS did the same :)