They both refer to wing movements here, but they don't have the same meaning.
'Flap' suggests a larger and possibly slower movement. 'Flutter' is a rapid succession of small light movements. 'Flutter' is what a butterfly does.
The difference is clearer if you think about what a person might do. You can flap your arms, because arms are large and fairly heavy limbs. However, you might flutter your eyelashes - like a butterfly - because eyelashes can make a lot of very light movements in a short time.
There are many verbs in English ending in '--tter' which suggest a light repeated movement : twitter, flitter, pitter-patter, glitter, mutter, spatter, splutter, jitter, skitter, titter, totter, scutter, for example.