What is the difference between the adjectives "live" and "alive"?

Generally, live is an attributive adjective, and alive is used as a predicate adjective; in other words, live is usually placed directly before the noun, and alive is generally not.

These are live goldfish.
These goldfish are alive.

Lexico's definition of live (adjective sense 1) and alive (sense 1) are "not dead or inanimate; living" and "[predicative] living, not dead".

There are several other differences in shades of meaning, some of which you can figure out by looking at the rest of the definitions, but this is the main difference. There are also exceptions to this rule; for example, if you are talking about real-time broadcasting, electrical wires, or ammunition, you always use live, even in predicate position.

This is live television.
Watch what you say; this television broadcast is live.
Live from New York, it's Saturday Night!

It sounds as if you are trying to convey a binary status such as active and inactive. This is one of the many meanings of live

2.: exerting force or containing energy: as
a : afire, glowing live coals
b : connected to electric power
c : charged with explosives and containing shot or a bullet live ammunition;
also : armed but not exploded a live bomb
d : imparting or driven by power a live axle
e : being in operation a live microphone

Each of these uses suggest the ability to turn the status on or off. This is a common usage in American English.

It is true that alive can also convey active status

2 . a : still in existence, force, or operation : active kept hope alive
b : still active in competition with a chance of victory must win to stay alive in the playoffs

However, this usage is not common where there is little direct control over the alive status. One would not say an alive circuit or alive ammunition. In fact, alive is more often used as a predicate adjective than an ordinary modifier.

The passengers were alive!