I just bought an old Commodore 64 from a used electronics store. There was a box of cassettes next to it so I grabbed a handful, only to find out now that they all say "VIC 20" on them. Will the Commodore 64 play VIC 20 software?
I used to have both (and a C16 as well). Most Vic20 software will run on a C64 without problems (though I only had a few Vic20 games).
If you're having problems with the tapes, that's a common problem, demagnetize the head, you may even need to realign the head, but rather don't tamper with it until you're sure that's the problem (most C64 repairs were casette-players that the users tried to tune without knowledge of how that actually worked).
No, it won't work as the hardware is different. They use the same type CPU (although the 6510 in the C64 is a modified 6502, but still compatible). The graphics chip in the VIC 20 (which is more rudimentary than the C64's) doubles as a sound chip, while the C64 has its own dedicated and more advanced sound chip. And as mentioned above, memory adress and peripheral address locations on the two are completely different.
They use the same version of CBM basic (V2), but the screen size, sound, and graphics capabilities are completely different. So in summary, simple basic programs using print statements for output might work similarly enough. But just about everything else, and pretty much anything you would consider to be a game, would not work from one to the other.
(disclaimer: never used any of those machines, this is from searching around)
They might not be completely compatible, because the design of the machines is different. Judging from this:
Because the VIC and the PET use completely different memory maps, PEEK and POKE commands were not compatible and because the VIC had only a 22 character screen while the original PET's had 40 character screens, only VERY rudimentary Basic 2.0 software would function on both machines. However, the VIC-20 was generally peripheral compatible with most Commodore 64 devices.
The C64 and VIC also use the same disk/tape format, however, you can NOT run C64 software on a VIC, nor can you run VIC software on a C64.