In practice, "scientific computing" meant floating-point number-crunching like physics simulations, and "business" computing meant I/O-oriented record processing, such as doing the weekly payroll.
On machines targeted at the scientific market, binary arithmetic was more common, floating-point hardware was usually standard, error correction hardware less common (since once-off errors don't usually have the same consequences in a simulation vs. a bank account) and IO throughput, particularly from multiple sources, was not usually prioritized.
On commercial machines, there is more emphasis on decimal data, string processing, and BCD arithmetic instructions were usually provided. The early machines of this lineage were indeed in the tradition of unit record processing equipment, and they were designed around that environment. More emphasis was given to IO and in particular record-oriented processing (punched card and magnetic tape), since a wide variety of disparate datasets might be frequently used, compared to the more typical scientific "load and compute" job.
For IBM in particular the split originates at the very beginning of computing, in their first two designs, done by different branches within the company. IBM had been contracted for a high-speed computer, and ultimately designed the IBM 701 "Defense Calculator", with the US government's number-crunching needs being the primary intended market. It was a binary machine, high-speed and oriented towards high-speed magnetic tape IO. Its successor, the 704, would have built-in floating point math as well.
At the same time, the unit record equipment branch of IBM was developing the "drum machine" which would ultimately be the IBM 650. It was a much smaller, slower machine, primarily targeted as a programmable replacement for unit record equipment. It was a decimal machine and oriented exclusively towards processing punch cards.
This split would continue for well over a decade, with later families of semi-compatible machines in both lines. By the time of the IBM System 360, companies had realized most customers did at least a bit of both kinds of work on their machines, and that memory size, CPU size and IO needs could be very different for different customers. That was part of the motivation for merging IBM's product lines into System 360, and most System 360 models could have both the "commercial" (decimal) and "scientific" (floating point) instructions, at least as options, and the very high-end machines had both by default.