The events in a hypothetical football match are:
- 45 mins - half-time (score 1-1)
- 90 mins - end of normal time (score 2-2)
- 120 mins - after extra time (score 3-2)
Would it be correct to say that score was 2-2 at full-time?
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Yes, the following statements would be correct:
Here is a quote from a wikipedia page for terms used to describe overtime in sports:
In association football knock-out competitions or competition stages, teams play an extra 30 minutes, called extra time, when the deciding leg (or replay of a tie) has not produced a winner by the end of regulation or full-time.
Now of course, there are plently of different valid ways of referring to the score at either the end of regulation or extra time and there isn't a single correct way, but at least with these terms people will probably know what you are talking about and not be confused.
There's no reference to specific term to be used in the Laws of the Game, especially in the Law 7: the Duration of the Match. Your best bet would be to refer to the rules/regulations of the particular tournament that you're interested in, but again it's unlikely that any tournament rules would include such terminology definitions.
Answering your question, I would say yes. By "full-time" people usually mean the score at the end of 90 minutes but it adds some ambiguity, so the terms "regulation time" or "the end of regulation time" are more preferred. Here's the WikiPedia article explaining respective terms.
To refer to the end of 120 minutes, people use "after extra time" (a.e.t.). Here's an example from UEFA Champions League 2013/14 Final match report.
To refer to the end of game after 120 minutes and penalty shootouts, people use "after penalties" or "on penalties". Here's an example from UEFA Champions League 2015/16 Final match report.
But again, there's no central repository which stores respective definitions of minor football terms. In Russian, for instance, to refer to the end of 90 minutes people mostly use "в конце основного времени" which means "at the end of main time", so what I'm saying is such non-regulated terms can have many different forms.