Context: Suppose you have just arrived at a cinema and say:
- A lot of people have sat, waiting for the movie to start.
- A lot of people are sitting, waiting for the movie to start.
What is the difference between these two sentences? Which one is correct?
What meaning does each one of the "are sitting" and "have sat" exactly convey to a native English speaker?
Both are grammatical and idiomatic although “have sat” is somewhat odd.
Many people have already sat [and are] waiting for the movie to start
emphasizes that the activity of putting yourself into a seat happened in the past and that the activity of waiting is happening now. It is difficult to imagine a situation where this emphasis on the different timing of two related activities would seem necessary in the context of seated people waiting, but other contexts might warrant it.
Many people are sitting [and] waiting for the movie to start.
Here the emphasis is all on the present. It is of course true that to be in a seat implies the prior act of lowering your posterior into the seat, but the focus is on the relatively non-strenuous activity of sitting in a chair while waiting.
The meanings are overlapping and very slightly different. It is primarily a matter of emphasis.
You should picture an auditorium with seats. Either form would be understood to mean that "a lot" of people have been admitted to the auditorium and at least temporarily were in their seats. The auditorium would be understood to have progressed some large fraction of the process of getting everybody in and seated.
The "have sat" form emphasizes the action of going from standing to sitting. It implies they are still sitting without actually stating it. It could mean that the people involved have been assigned to their seats, were in them for some time, but are not necesssarily still in them. For example, some of them may have their tickets and are in the auditorium just standing around. Or they could be making a trip to the popcorn stand or the bathroom or some such thing.
The "are sitting" form emphasizes the action of currently having their bottoms in chairs. It explicitly says the people involved are currently in the chairs.
However, these would nearly always be used without any strong care. That is, the person saying them is unlikely to go into the auditorium and check if everybody is actually in their seats. So, for most purposes in most situations, you should expect that either form could be used.
While sit can refer to the act of moving to a sitting position, it is far more often used as a stative verb meaning "be in a sitting position". If we want to refer to the movement, we generally say sit down.
So, the perfect have sat nearly always refers to an extended period, extending up to the present - often with a time:
We have sat here for two hours now.
I think in your case what you want is
A lot of people have sat down, waiting for the movie to start.
That is possible, but focuses on their act of sitting, so I would say that
A lot of people are sitting waiting for the movie to start.
I have omitted the comma in the second case, because it feels more natural without it. "Sitting waiting" is quite a common expression, though I'm not sure how it's best analysed.
(In Yorkshire, where I live, many people would say A lot of people are sat waiting for the film to start, but that is not standard).
As others wrote, there is the question of emphasis.
Picture those phrases in context. It gives nuance. What you say is (sometimes? often?) implicitly in contrast to what you omit, and/or to what you would otherwise omit (and, because of that, saying it conveys information).
In concrete, if you say "people have sat" to convey information then it probably means "people have sat when otherwise they would not", for example they have sat because they have been waiting for too long and are too tired to remain standing. That would be strange in a cinema, where people usually sit; but not in a concert, a rally, a long queue, etc.
Of course, if from context it is clear that the speaker chose this turn of phrase without any particular care, then no such nuance is present. :-)
