Русско-англо-русский юридический словарь

A coat of arms is a heraldic visual design on an escutcheon (i.e., shield), surcoat, or tabard. The coat of arms on an escutcheon forms the central element of the full heraldic achievement which in its whole consists of shield, supporters, crest, and motto. A coat of arms is traditionally unique to an individual person, family, state, organization or corporation. (Wikipedia)

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)