Русско-англо-русский юридический словарь

A national coat of arms is a symbol which denotes an independent state in the form of a heraldic achievement. While a national flag is usually used by the population at large and is flown outside and on ships, a national coat of arms is normally considered a symbol of the government or (especially in monarchies) the head of state personally and tends to be used in print, on heraldic china, and as a wall decoration in official buildings. [...]

For a symbol to be called a "national coat of arms", it should follow the rules of heraldry. If it does not, then the symbol is not formally a coat of arms but rather a national emblem. However, many unheraldic national emblems are colloquially called national coats of arms anyway, because they are used for the same purposes as national coats of arms. (Wikipedia)

What exactly is the difference between a coat of arms and an emblem? For example, why is the seal of the USA a coat of arms, while the state emblem of Soviet union an emblem?

A coat of arms has a shield. This shield may be depicted alone or with additional elements, like the ones coats of arms usually have, i.e. helmets, mantling, and a crest. Or even more, like supporters, crowns, mottos, etc.

Now that's not everything. All this has to adhere to the rules of heraldry. E.g., a photograph on a shield is not a coat of arms. A coat of arms is a unique symbol (at least unique in one jurisdiction), representing one or several (related) persons, or any legal person (like a club, a company, or an administrative unit). Also, coats of arms are defined by their blazon, not by one specific image, so they can be drawn in different styles and are still the same coat of arms. This is true even for countries and other territorial units, who in practice often use just one specific version of their arms.

The seal of the USA contains a coat of arms in the centre: there is an eagle in a typical heraldic pose, with a shield on it. The shapes and colours on the shield adhere to heraldic rules.

The Soviet emblem on the other hand, does not have a shield or a crest. So it's not a coat of arms. I'd say, coats of arms are a subset of emblems, so we call it an emblem. The Soviets deliberately didn't want to use a coat of arms, which they saw as aristrocratic. But they still had an emblem, which they used where other states use their coats of arms. (reddit)

The State Emblem of the Soviet Union (Russian: Государственный герб Советского Союза, tr. Gosudárstvenny gerb Sovétskogo Soyúza, IPA: [ɡəsʊˈdarstvʲɪnːɨj ɡʲerp sɐvʲˈetskəvə sɐˈjuzə]) was adopted in 1923 and was used until the dissolution of the Soviet Union in 1991. Although it technically is an emblem rather than a coat of arms, since it does not follow traditional heraldic rules, in Russian it is called герб (gerb), the word used for a traditional coat of arms. (Wikipedia)