Correct term for “string consisting of words”
If definition (1) is intended for any sequence of characters, I would
simply call it string as you suggest, but I would call it word or
lexeme if it is intended to be words of a language.

Regarding definition (2), it depends again on what you are expecting
to consider. If it is any sequence of words, usually meaningless, with
a variety of separators, the name text would do fine, and I would
not worry too much about computational linguistic since the only
meaningless piece of text that matters in CL is "Colorless green ideas
sleep furiously".

If it is actually intended to be a sentence of a language, then you
might call it sentence. I feel that text would rather be used for
larger pieces of discourse. You should be careful though that is is
not confused with sentence meaning a string of words. Speech
processing people may speak of utterance, but it may be
inappropriate for your use. They use also sentence, which they
structure into word lattice when the separators are not clearly
identified, which amounts to a word sequence or word string if they
are clearly identified.

This disctinction may also depend on whether your separators are one or
many, and whether they have a role.

In other words, it is hard to give you a precise answer without more
details on what you are doing. I first tried, and then realized that
it led me to make unwarranted assumptions about what you are doing.

The one thing that is really important is that you are very clear
about your definitions. And if you can motivate your terminology
choices, that may help the reader. I am still wondering why the borogoves had to be so mimsy.