Assuming you mean the verb (both words can be both noun and verb), Oxford says this:

1. Push suddenly or violently in a specified direction

Is there a particular context that interests you?

I hardly hear the word thrust ever so I was wondering why it's used here. Is it just a more elegant way for saying throw or push?

A style-conscious writer will tend to use a wider vocabulary, hence you might see e.g.:

In your example, the simpler alternative would be throw rather than push.