Pardon comes from French, and it is used in the same way in Romanian "excuse me, I'm sorry". It is used when you bump into someone by mistake, or you want to pass but that person blocks your way, you raise awareness. (native speaker)
"Scuze" is informal. It is the equivalent of Sorry. It is the short form of "îmi cer scuze" I appologize. "Mă scuzați" is formal = Excuse me. "Scuză, scuze=excuse, excuses" noun.
The way you use it can mean different things. Some people, when they walk through big crowds, say, "Pardon me." Which may mean 'Excuse me.' But also can mean 'I am sorry.' English is a hard language
So, "scuza" is a short, informal way to say "scuza-ma" -imperative form? [Those "a" letters should be with that small u-shaped mark above (i.e., the "a-breve" [?]) But, of course (?), the infinitive "a scuza" has no such mark.]