Apple of course invented the personal computer with the Apple 2. IBM a long time thought - no market and with the privatisation of the computermarket. IBM brought 1981 their Personal Computer. 1985 Apple brought (after LISA) GUI on the market. IBM lost against the Compatibles and the rest ist history. 

The difference between Homecomputer and Businessmaschines was clear for the homecomputer users. Homecomputers were cheap, colorful, had sound, modern (GUI) and you could play with them. So they were designed for ‘fun’. And they came all in one - as one consumer product. So it was ‘identity’. Clear that the Amiga was first designed as an Console. On the hardware side the homecomputers didn't use the ugly intels like almost no Arcade-Console-Maschine did. The question here why? Perhaps because the most of the Software had to be coded in Assembler? 

One of the big question was: Is the Macintosh a Homecomputer? One answer it was to expensive for beeing a homecomputer. Perhaps the homecomputers were the cheap versions of the macintoshs.