Every bird has its own unique way of flying.
Take the sparrow for example - it's unimaginable to take a shot of it in free flight. It flies like a little ball of feathers, bouncing up and down in such an unpredictable fashion, that the best attempts at catching it can't match even a photo as bad as the one bellow* :
The swallow on the other hand is much more structured, although it's still very fast, very hard to catch.
The flight of the swallow consists of series of straight lines of different lengths between random spots in the air, joined by sudden harsh turns.
Here it is in the photo above, twisting it's body in the middle of a turn so rapid that it almost resembles the vertex of a 90 degree angle.
If we drew an imaginary line of light to trace it, the flight of the swallow would look just like a lightning in the rain.
It's easier to take a shot of a bird that's standing still, but without it flying, a part of the bird is missing.
* Of course, if you ask the internet for a photo of a sparrow in flight, it provides plenty. Almost all of these are done in a controlled manner, where the camera is preset to capture a specific spot and a lure is used to guarantee that the bird will pass trough there, that's why almost all such photos are either a landing or a take-off happening immediately next to the lure. Occasionally - a fight between two birds, which is way easier to focus on, because it doesn't move around too much. And the remaining few of those photos ... well it might be just luck or there might be a photographer out there who's reflexes with a camera are THAT quick.