When did dial up change to high speed?

Dial up did not change to high speed. This may have been a misunderstanding of DSL.

This refers to connecting to either a network, or most likely the internet, using an analog modem over a standard analog phone line. It is also called dial-up networking or dial-up Internet.

Analog modems transfer data by taking binary bit values of data from a computer or networked node and transmit them by pulses of sound over standard analog phone lines. The term modem represents the MODulation and DEModulation from digital to analog. The modem first sends either pulse or tone (DTMF) dialing to ring the receiving line, then both modems use tones to negotiate compatible communications, then enter into a steady stream of data transmission.

Analog modems most popularly started at speeds around 75, 110, and 300 baud (bits per second). They eventually increased to 1200, 2400, and finally 9600 baud (bps). By using software compression, speeds of 14400, 16800, 28800, and 33600 baud (bps)were achieved. Lastly, the speeds said to be 56K (56000 bps) were developed initially by the incompatable X2 and Flex standards which were merged into the V.90 standards. They never fully reach 56000bps, but were considered of that class of connection speeds.

High speed connections, such as Internet connections, were generally referred to as broadband. Broadband could be interpreted as any remote network data connection speed above 128kbps (128000 bps). This includes ISDN, the various forms of digital subscriber lines (DSL) signaled over standard phone cabling, co-axial cable Internet service, leased lines such as T-1 and T-3, and most everything telecommunicaiton companies use.

It is possible that one could consider one of the various forms of DSL Internet connection lines to be considered "dial-up" because it uses telephone cabling. However, DSL signalling is not standard analog telephone line signaling. There is not a dial tone, there are no phone numbers dialed, and one is analog while the other is digital. It is simply coincidental that they both use a pair of copper wires from telephone poles that run down a long cable into a home.