Take my photo, take a photo of me

Please tell me, is there any difference when saying take his photo and take a photo of him? To me, the first one sounds awkward.

"Take his photo" implies to me that it could be for a specific purpose or part of a process (for a journalistic reason, for documenting something, etc.):

The police took his photo, then took his fingerprints.

Last week at school, they took my photo for the yearbook.

"Take a photo of him" is used when it's done more in the casual, spontaneous sense of photography:

We took a photo of the protesters during the demonstration.

Both are possible, depending on context. In BrEng both 'picture' and 'photo' occur (but you don't often hear 'snap' any more.)