The angle of view realized by the camera is a product of sensor size and lens focal length.
The venerable 35mm full frame film camera sports an image that measures 24mm height by 36mm length. The corner-to-corner (diagonal) measure of this rectangle is 43mm.
The 1/2.3 digital chip produces an image 4.55mm height by 6.17mm length. The diagonal measure of this rectangle is 7.67mm.
The angle of view most often published is actually the diagonal angle of view. This value is the widest. Mount a 7.67mm on your 1/2.3 camera or mount a 43mm on a full frame and the angle of view for both will be 53°. Yes, both yield the same. (TV sets are sold by their diagonal measure because this value is the longest). Perhaps the diagonal measure is the least value and the horizontal is the most valuable but bigger is better in the world of advertising.
Also, mounting a lens with a focal length about equal to the diagonal measure yields an angle of view of 45°. Such a lash-up is considered the “normal” lens for that format. Mount a shorter lens then “normal” and you are in wide-angle territory (technically about 70% of “normal”. Mount a longer then “normal” lens, you are in telephoto territory (about 2X of “normal” or longer).
Bottom line: Angle of view and wide-angle – normal – telephoto is dependent o the combination of sensor size and lens focal length.