Email programs generally send what they get, unless the picture is too large - then they don't send it. The app you're using in the camera to view it is probably resizing it to fit the screen.
If you use an EXIF editor you'll see the size of the actual picture in the file. (In pixels, not in inches - picture files aren't measured in inches, since they can be viewed or printed in any size you want.) If it's a 320X480 picture, you can't blow it up much before you lose detail. If it's 2560X1600 ... well, that's higher resolution than a 65" TV screen (1080p is only 1920X1080), so you could make a pretty good 16X20 print.
Any picture can be made to fit even a small screen phone. And any picture can be printed 5 feet wide. But if you print a low resolution picture too large, you're going to see the pixels from pretty far away. In Grand Central Station, in NYC, Kodak has some transparencies high up on the walls. They were shot with standard 35mm film. From the floor, they're pretty nice pictures, but if you got up close, you'd see the equivalent of huge pixels (silver grains) in them. So "how large" doesn't really count in pictures, It's "what's the resolution" and "what's the viewing distance"? A huge low-res picture far away can look "smoother" than a higher res picture close up.