Terminology for sub-sequences

I'm just wondering what the proper names are for a few things. Clarification would be appreciated please.

Suppose I have a sequence:

1,1,2,3,5,8,13,21,34,55,...

Now suppose I construct a subsequence of only the even terms: 2,8,34,... Firstly, that is considered a subsequence, right? Or is it something else? Is it right to say that it is a "subsequence of sequential even numbers"? Or how should I say that?

Now suppose I construct a subsequence of a few terms that appear together in the sequence: 1,2,3,5 and I wanted to describe such a subsequence. I would say, "let a_0, .. , a_3 be a ?? subsequence".. where ?? is one of {consecutive, sequential, adjacent, neighboring}. How do I refer to that to distinguish it from the first subsequence I built? Or if I just want to say, "let a,b be two ___ terms of the sequence".

When we're talking about integers, I would say that 1,2,3 are consecutive integers, 2,3,5 are not consecutive but they are sequential with respect to the Fibonacci sequence. Is that right?

Thanks in advance.