What is the difference between crème anglaise and crème pâtissière?
Crème Pâtissière is a thicker mixture, and is usually used for filling a pastry. It would be rolled into, or injected into something that would then be baked. As such, it needs to be thicker, so as not too leak out, and usually more flavourful, as it is the main flavour in the pastry.

Crème Anglaise is what the English would call custard. It is usually served as a "sauce" for sweet dishes. A classic dish would be apple crumble, served in a bowl with custard around it. The custard is there to add richness, and complement the flavour of the cake, and is therefore usually more subtle in flavour.