Can somebody explain clearly what is the difference between 'draw' and 'pull'. In the excerpt below, if I change 'drew back' to 'pull back', Google gives different meanings. If I change 'pull together' to 'draw together' Google translates them the same. Such verbs come across in any text very often. What do I need to know when I can replace these verbs without losing meaning and when I can't? I have learned to translate them, but I can hardly use them correctly in English.

> 
> Canute **drew his hand** back from the latch as though it were red hot. He
>  was not the kind of man to make a good eavesdropper, and he wished he
>  had knocked sooner. He **pulled himself together** and struck the door
>  like a battering ram. Mary jumped and opened it with a screech.
> 
> 
> 

Here is the other example. What does 'drawing out' mean or would 'pulling out' mean? By the way I can 't find a suitable translation for '**power of drawing
out the social side**'. What does it mean?

> 
> But he was not a social man by nature and had not the power of **drawing
>  out** the social side of other people.
> 
> 
> 

On the Divide
by Willa Cather