Learn English – the difference between “I just got out of the bathroom” and “I have just gotten out of the bathroom”

The Oxford dictionary describes stench as:

A strong and very unpleasant smell

It describes stink as:

A strong unpleasant smell; a stench

So according to this, both words mean the same. I found also that both have the same etymology. They arise from the Old English stenc.

I was wondering if there were a shred of difference in their meanings but I am not able to find any. An English professor, very long ago, had told me that no two words in the English language have the same meaning. They may have similar meanings, but not same. But here we seem to have refuted his ideology.

Both are grammatical. Both are fully idiomatic. Both can describe the same set of circumstances, and be used in the same context.

As usual with questions of aspect in English, the choice is a matter of how the speaker wishes to present the temporal focus.

If the speaker uses the past infinitive here (to have started) they are setting the temporal focus later than the time the lesson should have started. If they use the unmarked form (the simple infinitive to start) they are not setting the temporal focus.

In this case, I can't see any consequences in setting or not setting the focus, and the sentences are interchangeable.