"hear us sing" vs "hear us singing"

(Grammar Questions I Couldn't Answer)

Actually this question doesn't come from the students--this is a question I asked myself.

The question came to me while preparing movie worksheets for "The Secret of Nimh". *

In preparing these worksheets, I give the students 10 vocabulary words to listen for.  I introduce the dictionary form of the vocabulary word first, but then also show the form of the word that will appear in the movie, and show the grammar.

For Worksheet part 2, the following dialogue appears:
"I haven't found Miss Right yet. But when I do, the whole world will hear us singing."

I selected "singing" as the word the students were supposed to listen for.
On the slideshow, I showed them "sing" first, and then tried to introduce the context for "singing".

But what is the context here?  Is this a gerund?  A participial phrase?
And furthermore, unless my native-speaker intuition is betraying me, "singing" is not obligatory in this context.  It could also be "the whole world will hear us sing".  Right?
So then what is the difference between "the whole world will hear us singing" and "the whole world will hear us sing" ?



* I haven't posted these worksheets on this blog because the movie is still ongoing in my classroom.  But once I finish the movie, I'll post all my materials for this movie