I believe the one labeled “Commodore 64 Personal Computer” is the Commodore 64C, which was a redesign of the original C64 using the style of the C128. There were minor differences, but the intention was 100% compatibility with original software.
The '''C64C''' (aka C64-II) was the first C64 which didn't have a breadbox cabinet.
The (almost) white color complied with the color of the C128(D) and also the cabinet was similar to the C128 (apart from the missing numeric pad).
* In the year 1986 the C64B and C64B3 boards were assembled to the C64C (C64-II). The graphic symbols of the keyboard are printed on the front of the keys.
* From 1987 on only the smaller C64E board was assembled. The graphic symbols are printed on the top of the keys. So it was possible to identify which board was assembled without the need to open the cabinet.
The sound chip (SID) now had the naming ''MOS 8580''. A sound difference between the 6581 and the 8580 is audible.
The C64E board was significantly higher integrated.
* The RAM memory now resides in 2 instead of 8 RAM chips.
* The two 8k byte sized ROM chips for BASIC and kernal have been joined on one 16k byte sized ROM chip (251913-01).
* The PLA chip and some TTL chips have been integrated into a 64 pin chip (251715-01 or 252535-01). The "252535-01" contains the color RAM as well.
Through this the production costs could be reduced and so the C64C could be offered for a lower price than the original C64 "Breadbox".
[https://www.c64-wiki.com/wiki/C64C|Source]