The term "personal computer" can mean one of two things. Gates invented neither.
The original meaning (I deal with the other meaning in the next myth) was simply any small computer over which the owner had complete control and was not connected to a network, as opposed to a mainframe or mini-computer which would be shared by a number of users via terminals. Personal computers were also called "micro-computers", "micros", "desktop computers", and even "desktop calculators" (the last to avoid frightening people with the word "computer"). When they became consumer-cheap, and aimed at that market, they were also called "home computers".
Far from inventing the personal computer, Microsoft's first contract was writing software for one which already existed. They (Allen, Gates and Davidoff) wrote a version of BASIC for the Altair 8800, which was launched in 1975 as a kit by a company called MITS. By this time there had been micros on the market for about a decade, starting with the Olivetti Programma 101, and including the Hewlett-Packard 9100 and 9800 series and the the Wang 2200. BASIC is a high level programming language and operating environment which had also been around for ten years on mainframes, minis and micros. While it was a creditable achievement for Microsoft to have written a version for the tiny Altair, no invention was involved.
Here is a young Gates with Paul Allen, his co-founder of Microsoft, and a collection of early personal computers. Allen looks about a hundred years older than Gates, but in fact is only two years his senior