I strongly suggest to refer to this great post, that surely helps in make issues clear about file saving.
Anyway, saveRDS could be the most adequate for you. The difference more relevant, in this case, is that save can save many objects to a file in a single call, whilst saveRDS, being a lower-level function, works with a single object at a time.
save and load allow you to save a named R object to a file or other connection and restore that object again. But, when loaded, the named object is restored to the current environment with the same name it had when saved.
saveRDS and loadRDS, instead, allow to save a single R object to a connection (typically a file) and to restore the object, possibly with a different name. The low level operability makes RDS functions more efficient, probably, for your case.