In The Grammar I Am Teaching From Shurley The Word Laughing Is Considered A Gerund O 2840834

In the grammar I am teaching from (Shurley), the word ‘laughing’ is considered a gerund (one of three types of verbals) in both of the following sentences:
1. The laughing child tripped.
2. He heard the child laughing.
As used in the first sentence, laughing is clearly an adjectival gerund, but in the second it seems to operate much more like a verb, an action. The two uses seem very different to me. I remember studying this years ago and finding this ambiguous but I don’t recall receiving a satisfactory explanation. Could you help clarify th matter for me so that I will better be able to pass this on to my students?
A further matter concerns the classification of the word learn in the following sentence:
Conversing helps the children learn French.
Is this simply an infinitive?