Is a photo is also a picture?

Both of those sentences are correct when referring to a photograph. All photographs are also pictures, although it is not necessarily true that all pictures are photographs. Picture is a more general term than photograph. A picture can be a photograph, a painting, an engraving, a lithograph, a pen and ink drawing . . . just about any form of representational art (excluding sculpture). The expressions photo gallery and picture gallery are often used interchangeably online, but it should be used more carefully in other situations, because in real life, a picture gallery might not refer to photographs. Online, all picture galleries contain digital images, but in real life, the images may not all be photographs.

I use them interchangeably.

Yes, me too.

I think most people do.