As there is overlap between these two terms. Electricka explains here the
basic nature of each and the way
in which The Muses distinguish between them:
Contest—As used here, a contest
is a structured, organized race, conflict, or other competition between
rivals. Contests may result in strife or arguments, disputes, or other
controversies; they may arise over a controversial question, issue, or
rivalry. If there is a prize, it may be concrete (cash, a sponsored trip,
a scholarship) or it may be abstract (the showing of a winner's art work,
honorable mention).
In this feature, contests are limited to struggles for victory or
superiority in which contestants personally demonstrate or exercise an
art-related skill or craft for whose excellence they can win during the
period in which the contest is actively underway. The contestant wins by
using the skill in direct combat with opponents. The demonstration may
take the form of personal activity, like sketching in front of an audience
or playing a piano; or it may take the form of passive activity, such as
exhibiting a portrait or submitting a recording.
This definition is performance oriented; it includes contests that give
awards for things participants do during the contest or things they make
or submit specifically for the purpose of winning; it excludes contests in
which "victory" is measured by generalized achievements, skills,
contributions, or talents—for example,
contests that grant lifetime achievement awards are not part of this
feature. Another way to describe this aspect of a contest: In this
feature, contests are more like jousts and less like Pulitzer prizes.
Tournament—A tournament is a
trial of skill in some game, in which competitors play a series of
contests, such as a chess tournament, a crossword puzzle tournament, a
spelling bee, or the like. The primary difference between a tournament and
a contest is that a tournament consists of a series of strongly related
contests.
A tournament may be fought between individuals, groups, or teams. It
may pit individuals or teams from different places, nations, or cultures
against each other; or contestants may be defined by almost any other
criteria.
Tournaments are more intricate than contests; they call for more effort
on the part of organizers and have a more complex structure. Why? Because
in a tournament there are multiple contests that need to be organized,
each with its own demands, and because each contest in a tournament is
functionally and conceptually interrelated to all the others. For example,
a typical crossword tournament consists of a series of preliminary puzzle
sessions designed to eliminate less skillful entrants and identify
finalists; all the individual contests are capped by an extra, overall
session in which winners are established.
Historically, a tournament was a contest or martial sport in which two
opposing parties of mounted and armored combatants fought for a prize,
with blunted weapons and in accordance with certain rules; it was a
meeting that occurred at an appointed time and place for the performance
of knightly exercises and sports. Although times have changed since these
good old days, modern tournaments and contests in the arts are not
dissimilar in many respects from their earlier counterparts. Although
modern tournaments are not as physical as their predecessors, they can be
just as hard fought and strenuous; rivalries can be just as intense or
bitter.