As stated in Guide to Grammar and Writing, they are called parenthetical elements or added information. To set off these elements, we use two commas. It simply means that the part of sentence is set off with two commas is there to give us additional information removing which would not affect the meaning of the sentence.
Use a comma to set off parenthetical elements, as in "The Founders Bridge, which spans the Connecticut River, is falling down."
By "parenthetical element," we mean a part of a sentence that can be removed without changing the essential meaning of that sentence. The parenthetical element is sometimes called "added information."
But how to differentiate them from those conjunctive adverbs like :however,on the other hand, or they are somewhat similar?
However, Nevertheless... etc. talk about the other aspect of the matter said earlier (-say "I like you, however, I cannot marry you"). They have no connection with parenthetical elements because the latter ones are additional information, and the clauses you put after what you call adverbs are essential parts of the sentence.