A standard lens or normal lens is a general-purpose lens which has a focal length approximately equal to the diagonal of the film format used. These lenses have a field of view approximately equal to the human eye and are well corrected against distortion and curvature. The full "field of view" of a human eye is approximately 180 degrees on the horizontal, and this includes our peripheral vision. However, we tend to selectively focus on a field of about 55 degrees on the diagonal.
For 35mm-format (called "full format" in digital age!) the diagonal of the image (24x36mm) is 43mm. 43mm objectives are considered to have a "natural angle of view", as opposed to wide angle (short focus) lenses or telephoto (long focus) lenses. Interchangeable lens cameras began using 50mm, 55mm, and 58mm lenses, with very fast lenses (f/2 or faster) have been developed and thus the term standard lens may have been extended so far above 43mm since 50+ mm were a practical focal length for superb fast lens constructions. Fast standard lenses were the typical "kit lenses" sold together with rangefinder cameras, such as the Sonnar 50mm or the Summitar 50mm; and in the 1960s an 70s with SLRs for 35mm film. The reason was that the high lens speed gave a bright viewfinder image, meaning immediately an advantage in comparison with TLR viewfinders. The new mechanical automatics easing to focus at max. aperture and shooting at chosen aperture made fast standard lenses a good marketing argument. And there were fast lens constructions like the Planar which gave a model for good lenses which were promotionally effective to sell further lenses to the SLR customers. Thus the typical classic 35mm viewfinder cameras had lenses of focal lengths between 38mm and 50mm, around the "natural" angle of view, whilst the kit lenses for 35mm SLRs had a focal length between 45mm and 58mm, all with smaller angle of view but not yet recognized as "long focus".
In medium format cameras with larger image sizes, the standard lenses were 70-75mm (6x45); 75-80mm (6x6) or 90-105mm (6x7)