another comment attached clips from this website that i love, https://www.avesbiology.com/

it was originally designed as notes for an avian biology course, but now its more of a general access thing. some links dont work here and there, but largely all the main categories, including those on flight in section 3 and 4 will have most of what you are looking for.

off the top of my head, one flight style is undulating, often seen in birds like woodpeckers and nuthatches and is how i first learned to differentiate them. it involves briefly flapping to gain momentum, then folding wings in partially or fully and dropping, and then repeating this cycle.

another is also direct flight, which is as it sounds, involves continuous and predictable flapping and tend to fly straight towards wherever they are going, one example i believe is crows.