Is there a different grammatical term for "If I was" than for "If I were"?

Purely in terms of the terminology, then a distinction sometimes made is that:

• inflectional subjunctive is the type found in Old English, German, modern Romance languages etc, in which verbal inflection distinguishes subjunctive from indicative;
• periphrastic subjunctive is the type found (if you adopt this analysis) in modern English, in which subjunctive is distinguished from indicative by way of modal auxiliaries/other verbal constructions.

There's really no consensually agreed upon "wrong" or "right" answer to the question of whether English actually "has a subjunctive". If you adopt the analysis that "subjunctive" is the grammaticalisation of non-assertive force with a verbal paradigm-- which seems to be a close approximation to what the phenomenon is in Romance languages-- then it's fairly clear that English doesn't have such a phenomenon. (Saying that English has a past subjunctive on the basis of the form "if it were" is a bit like saying that English is a verb-final language on the basis of a phrase such as "Language does not a society make": it's proposing a paradigm on the basis of a rare exception.)

If you extend the definition to cover cases such as English "It is sad that he should leave", "David commanded that she leave" etc, then there are various issues to be considered which are typically glossed over in language learning textbooks:

• care must be taken to recognise where the similarities and differences actually lie between these phenomena and the inflectional subjunctives of French etc;
• it is worth thinking about what the motivation is for proposing "subjunctive" as a 'special case' of modal verb usage.

I believe some modernists call it simply the past form, because, for all verbs but to be, it is identical in form to the simple past, which expresses a reference to the past. I'd be the last person to recommend this term, but here it is.

Most people still seem to stick to the term past subjunctive. (I'm also under the impression that if I were is still de rigueur in most educated circles, not was, though there is bound to be considerable variation.)

Michael D.C. Drout in his book History of the English Language says the following about subjunctive mood:

Modern English has mostly lost the subjunctive form and replaced it with modal auxiliaries like could and would.

It’s my understanding that Old English made use of the subjunctive mood and that's why we still use “If I were you” in Modern English even though it appears incorrect. It’s a relic from our Anglo-Saxon roots.

Michael Drout has written a series of audio books on the English language (published by Modern Scholar). Since his background is in Anglo-Saxon literature and culture, he is a good resource for questions like these.