Info on moving from one visa to another: don't just let the first one expire in your passport, get it stamped as officially cancelled. My old school cancelled my work permit, but didn't get it stamped in my passport, and now it's a whole thing getting the stamp months later.
TLDR : Answer Summary
When transitioning from one visa to another in Thailand, it is crucial not to let the first visa expire in your passport. Instead, have it officially cancelled with a stamp in your passport. Failure to do so can lead to complications later. This advice applies not only to Education (ED) visas but also to Non-B extensions, as indicated by community comments.