Ackchyually, the Y2K bug was pretty different. A lot of software, for various reasons, took to representing dates as a two digit number. This meant going from 1999 to 2000 would make that software try to understand dates going from 99 to potentially various of other values, like 00 or 100.
We’re gonna have a different form of that on machines with 32 bit processors relatively soon. Past some time on Jan 19th, 2038, the epoch time, a count of seconds since Jan 1st, 1970, is stored as a 32 bit signed integer. At this time, it’ll run out of positive values, will overflow, and cause the internal clocks of such machines to go back to 1901. It probably won’t happen again after that, as the maximum date represented by the largest signed integer a 64 bit machine can store is 292+ billion years