This is correct.

And it helps explain why a 50mm lens... a "normal" or "standard" lens on full frame... But the same 50mm works so well as a "short portrait telephoto" on a crop sensor camera. (On an APS-C camera 50mm "acts like 75 to 80mm on full frame", while on a Micro 4/3 camera the same 50mm "acts like 100mm on FF").

The image below was shot with full frame camera, 24-70mm lens at 63mm... slightly telephoto, but the close distance leads to a lot of perspective exaggeration. Obviously, the horse's head isn't larger than it's body!



The effect can be used humorously, as I tried to do with the above shot. But most people won't appreciate being photographed in a way that makes their nose look big and their ears look tiny, so keep your distance and choose the appropriate lens for the purpose.

50mm on full frame (~30mm on APS-C or 25mm on M4/3) can be used for full length portraits of individuals or couples standing or for wider "environmental" shots that show a lot of their surroundings.

Anamorphic distortion is another effect that occurs with wide angle lenses that also needs to be considered. Parts of the subject close to the edges and corners of the image will be "stretched" and look deformed. Compare the two shots of this car, for example...



Both were shot with the same zoom lens on an APS-C camera... The lefthand image was shot with a 12mm focal length setting, while the righthand image was shot with 20mm. Positioning the car to the far left side of the horizontal images causes it to appear quite distorted... notice the size of the tires in relation to each other and the grill in relation to the rest of the car.

This effect looks even worse when people are placed near the edge of the frame, especially on the "long side" of the image... it causes effects sometimes referred to as "elephant legs" or "Hellboy arm".

Depth of field is another subject entirely, although it can be important for portraiture.

DoF is actually doesn't change with sensor format alone. If you use the same aperture, the same lens focal length and shoot the subject from the same distance, DoF will be identical regardless of the sensor size. However, because the framing of the subject in the image area will be quite different with the change in format, you would almost never do that. Instead, when you switch from crop to FF, in order to frame the subject the same way you either need to move closer to your subject or you need to use a longer focal length... or a little bit of both.

DoF does change when focal length or distance or both change. The result of the changes in focal length and/or distance is that at any given aperture FF "seems like" it's able to render about one stop shallower depth of field than APS-C, and about two stops larger than M4/3. This is also why it's very difficult to get shallow DoF effects with digital cameras that use really tiny sensors like 1/2.3". (Plus, this is nothing new to digital... same happened with film formats. When the same stop is used, but distance and/or focal lengths are changed, medium format film camera images look about a stop shallower DoF than 35mm film cameras. Larger format film cameras could render even shallower DoF effects. Conversely, small film formats like APS-C, 126, 110, disk, etc. have difficulty rendering shallow DoF.)