What is the difference between using a colon and a semi-colon to join two sentences?

I've seen a few questions on this site relating to semi-colons, which I believe I correctly understand, but what I'm not as clear about is colons. For example:

The man ate the apple; it tasted good.

Is this not correctly also written as:

The man ate the apple: it tasted good.

In this case, what is the difference between the two sentences?

In your example, the first one is correct but the second one is incorrect.

Use a semi-colon to connect two related independent clauses.

They took the money from the vault; they took it quickly.

The ideas are related, the clauses stand on their own, semi-colon is OK here.

Use a colon to separate equal things (like an '=' sign).

Just remember three things: be on time, bring the money, and come alone.

The things here = those three items.

Colon is a punctuation mark indicating

• that a writer is introducing a quotation or a list of items.
• that a writer is separating two clauses of which the second expands or illustrates the first.
• a statement of proportion between two numbers: a ratio of 10:1.
• the separation of hours from minutes (and minutes from seconds) in a statement of time given in numbers: 4:30 p.m.
• the number of the chapter and verse respectively in biblical references: Exodus 3:2.

Semicolon is a punctuation mark indicating a pause, typically between two main clauses, that is more pronounced than that indicated by a comma.

In your example, the colon is not what I would use.

Both can be correct. It depends on quite what you are intending to convey and the context surrounding the statement.

The first one shows two coupled actions with equal priority in the narrative. The semi-colon couples them closer than if they were two sentences, but the comparative effect depends strongly on the surrounding text, such as where they are in the paragraph, how big or small the paragraph is, and what else is being described.

The second example, using the colon, shows a more direct relationship between the clauses. They are not equal in this construct, but dependant. The second clause is the focus of the sentence, but again, the effect still depends on the surrounding text. Your second example would work well at the end of a passage where the apple is an important item and that it tasted good was a satisfying resolution.