There are several ways the term 3/4 is used in photography. They have various different meanings. Sometimes an accompanying word, such as portrait or view helps to provide some context, but sometimes the context of the entire discussion needs to be taken into account to identify exactly what is being referenced by the term.
In portrait photography a 3/4 portrait usually means the subject is pictured from the top of their head to somewhere between mid-thigh and just above the knees. This usage does not depend upon what angle the model is facing with respect to the camera, just that the upper three-fourths of the model's body is included in the photograph.
A 3/4 facial view, on the other hand, refers to the direction the model's face is oriented with respect to the camera. It is called a 3/4 facial view because about 3/4's of the model's face is visible in such a pose. The model is pictured facing about a 45º angle to the camera so that the far ear is just out of view. The exact angle will depend upon the physical characteristics of the model's face. In contrast, a 2/3 facial view turns the model's head a little further from the camera so that the far eye is very near the edge of the face with just a small border of flesh between the eye and the space beyond the face.
A 3/4 view portrait may be the same as a 3/4 facial that is a tight framing of just the face and neck, or it may include the model's face at about a 45º angle (far ear just out of view) but also with more of the model's body visible which may or may not be facing the same direction as the model's face.
The term American shot or American cowboy shot originated in cinema but is now also used in still photography. It is both a 3/4 angle shot where the model is turned about 45º from the camera and a 3/4 portrait shot that makes about 3/4 of the model's body visible. This allowed both the actor's face and the six-gun on his hip to be visible to the camera. It can also be used in a context without the model wearing cowboy attire or a six-gun. (Interestingly, the phrase was coined by French filmmakers as a derisive term associated with the American cowboy movies that they detested.)
Other photographic subjects besides human models are often photographed in 3/4 view which means the subject is facing about a 45º angle to the camera. Photos of railroad locomotives, classic cars, airplanes, etc. are often shot in 3/4 view so that both the front and sides of the subject are visible. Sometimes an elevation is also used so that the top of the subject is also in view. The elevated 3/4 view is often used in product photography as well.