1. I regretted not going abroad.

= I regretted that I hadn't gone abroad.
(Are both the same?)

2. I regretted to go abroad.
= I regretted that I would go abroad.
( Are both the same?)

Both sentences in #1 are the same, yes.

Sentence 2 doesn't make sense, but the last sentence does, although it doesn't mean exactly the same as the two sentences in #1.