The reference to 32/64bit is not in a sense, correct.
When you intend to format a drive, Windows will offer three different file systems.
FAT32 is an old file system. It is not very efficient, but it has greater compatibility with any other operating systems, which, for example, you may wish to run in a virtual environment.. This is possibly what you have in your old SSD?
The default is NTFS, which is the current and more efficient file system. Windows will, automatically, use NTFS for the main system drive and, also by default, for non-removable drives.
The third is exFAT. It is an up to date replacement for FAT32. It is slowly becoming more used than NTFS.