NEOS Cheese Paint v1 is the software that came with the C64/128 NEOS Mouse.  This software can only save to a tape drive.  For more information and some screenshots, check out the c64-wiki.

NEOS Cheese Paint v2 by d0c is a paint program for the Commodore 64.  Below is his post from CSDB describing the software:

This is the neos mouse & cheese pack for the C64(obvious the mouse is not included). This software was released in 1985. The mouse version will only work with a neos mouse, so if you dont have it use the joystick version. The disks include also six test pictures, these should be removed before you start using the program.

The only differences in the cheese paint v1 and v2 is that the v2 is for disk users, and v1 is for tape users. So the big change is the loading & saving.

The neos mouse is also supported in these programs: Arkanoid , Arkanoid II - Revenge of Doh, Operation Wolf(these is the ones i know of so far).