Motion pictures are a comparatively recent invention. Here's how these words evolved:
Film meant a thin coat of something (still does)...
extended by 1845 to the coating of chemical gel on photographic plates. By 1895 this also meant the coating plus the paper or celluloid. Hence "a motion picture" (1905); sense of "film-making as a craft or art" is from 1920.
Movie is a shortened form of 'moving picture'.
By etymology, it looks like these terms are applicable to any video, but conventionally they are reserved for productions released theatrically.
Apart from that you have documentaries, direct-to-video features, TV shows (formally, series) and so on.
Can "movie/film" ever ever be a cover term for everything that is filmed and released in theaters or on TV?
No, it can't.
EDIT: Since people have shown interest in the comments, here are my thoughts on Made-for-TV and Direct-to-DVD features (We're digressing here, as this is not part of English language and usage):
I must say I don't consider them the same as movies.
To back this up, I present a short summary of relevant criteria a production must meet to be called a movie according to the Oscars:
a. feature length (defined as over 40 minutes),
b. publicly exhibited by specified film formats.
c. for paid admission in a commercial motion picture theater in Los
Angeles County, (for our purposes, let's call it any city)
d. for a qualifying run of at least seven consecutive days,
e. advertised ... in a manner customary to industry practice, and
f. within the Awards year deadlines specified in Rule Three. (not
Films that, in any version, receive their first public exhibition
or distribution in any manner other than as a theatrical motion
picture release will not be eligible for Academy Awards in any
Nontheatrical public exhibition or distribution includes but is not
These features may be equally great in quality, and eligible for some other prestigious awards, but they are not movies in the classical sense.