Both 32-bit and 64-bit programs can be run on a 64-bit Windows. When a 32-bit program is run on a 64-bit Windows, a 32-bit emulator will be invoked to handle the 32-bit program.
The emulator will make the 32-bit application to think it is running on a 32-bit Windows and the same functionality that is accessible on a 32-bit Windows will also be accessible for the program on the 64-bit Windows. Normally it will be hard for the program to know if it is running on a 32-bit or 64-bit system.