I wouldn't worry too much about the vector representations one sees in basic training texts and the various mechanisms used to describe what is happening in the real world. At the end of the day, they are only attempts to simplify what is a fairly complex physical thing.
Basically, fluid forces come from momentum changes (although the forces are transmitted via the effect of fluid pressures on a surface) .. for low speed flow, if you can manage to cause the flow direction to change, you get some forces. Trick is to get the desired forces (viz., lift) at the expense of minimum unwanted forces (viz., drag).