There have been many theorists building vocabularies for discussing how film tells stories – a notable one is Roger Spottiswood, but a classic one is Sergie Eisenstein’s Film Form and Film Sense. By “language,” these theorists are drawing parallels to verbal language, stage language, dance language, etc. Arts such as these have systems, methods for project information, emotional or intellectual, just like verbal language has syntax, grammar, and the like. Some of the conventions of film language are the fade out/fade in practice to indicate passage of time, the cuts, swipes, etc., that “read” as changes in place, etc. The movie-goer does not say, “My, where did the house go?” when the shot of the house is replaced by a shot of the highway through dissolves or fade-outs – these transitions are accepted by the viewer as part of the film language, as a convention used by film to tell a story. Similarly, pans, close-ups, etc. are devices the viewer accepts. In early film history, the camera did not move, and audiences used to get sick when filmmakers tried to introduce into the film language the traveling-camera shot. In modern films such as The Matrix, film language has expanded to include time-changing conventions, stop-motion photography to “read” as time actually speeding up, etc.
Cinematic language can be defined as," a 'language' of images (visual and aural) that tell story without the use of words."
Cinematic language can also be considered to people as the vocabulary associate with cinema. For example talking about animation, shorts (short films), camera angles, diegesis, and many other words can be considered cinematic language. There are many terms in the second link below.