Your question presents a false dichotomy, as the answer is "both".
Solomon Slow's answer covers one side. The last mile lines were predominantly built to exchange voice to a central office and onward around the world, so "dial-up" was limited to what could be done with existing equipment in the context of long distance analog voice circuits. Throw in monopolistic practices by companies like Bell and the system becomes very constrained as you were not permitted to connect anything except a Bell approved phone. Pre-dating your 1990s time frame you would have had an acoustic coupler linking speakers and microphones, with no physical connection to the wires. Key is that these were long distance analog signals.
However voice was not the only option. If you ran a large enough site you more than likely ran other systems over the same last mile twisted pair wires. Serial protocols connecting dumb terminals on private networks over short distances easily transmitted at higher rates as they had none of the restrictions of long-distance voice circuits. A large enough institution would have dedicated circuits connecting to other institutions. While still slow by modern standards, this was far more capable than voice. The biggest difference is that these were typically shorter distance digital signals on the wire.
By your '90s time frame Bell had lost the fight and you could hook up a modem directly; at the central office equipment had improved the quality of the voice circuits; and the wire itself in many cases had improved. As examples many rural and other longer distance "last miles" had load coils installed which allowed analog voice circuits to be run farther, but were not friendly to digital signals. By the '90s load coils were getting removed, central office equipment was more capable and often encoded analog voice into digital backbones, and smaller equipment was getting located closer to customers. Old steel lines were switched to copper. Voice equipment and modems were getting better, but it was still fundamentally a long distance analog voice system.
However voice was still not the only option. For a price you could switch the analog voice line to a digital system. While modems were getting 2400-19200bps, ISDN BRI could run 2 x 64Kbps bonded channels on the same pair of wires, while ISDN PRI, T1, E3, and other protocols allowed much higher speeds on the same copper lines (though 4 or more wires rather than the 2 required for voice). Today I still occasionally come across T1 1.5Mbps circuits running on 2 pair (4 wire) phone lines in rural areas where this is the best connection available, often with bonding applied to net a 6, 9, or 12Mbps connection on "every phone wire coming into the building". The biggest difference was still that these were typically digital signals on the wire over short distances (with your provider routing to the wider world).
This trend continues of replacing the voice equipment in the central office and on the customer premise with digital endpoints while optimizing the copper lines by moving more central office equipment toward the customer. Today the last mile on copper VDSL2+ is often short to a DSLAM in a relatively close cabinet where the traffic moves to fibre. Interestingly, the wires no longer carry one or the other between voice or digital but rather carry both with filters separating voice in lower frequencies from digital at higher frequencies on the same wire.
Most of this comes from my own experience (also in Canada), so I'd gladly take improvements. I ran 300bps in the '80s, '70s era campus serial connections on mainframe in the early '90s, ISDN BRI in mid '90s, and pretty much everything else mentioned personally or professionally over the years up to my current VSDL2 bonded pair (which sucks, I used to have FTTH).
