This thesaurus entry says:
式 emphasizes the aspect of event while 儀式 refers to what happens during a 式 following a defined procedure (or the procedure/protocol itself).
Most ceremonies like wedding or graduation assume some general agenda, but it is not considered as a protocol. So those are generally 結婚式, 卒業式 etc.
On the other hand, an exchange of rings or drinking Sake in a specific way (in traditional Shito style weddings) can be called a 儀式.
Borderline cases are those that are extremely solemn like inheriting a throne or abdication, which I assume require a very specific procedure. These ceremonies themselves are definitely 式(典), but could be called 儀式 as well.
I'm not at all familiar, but as another example, communion can be a 式 as an event, but the act of receiving the bread is definitely a 儀式.