Sometimes you can use a semicolon where you use an em dash, but that's only coincidence: They serve different functions and usually you can't.

Rae bought all the candy at the store - Milky Way, Reese's, M&Ms, everything - and set out for Kay's party.

That can't be rewritten as,

Rae bought all the candy at the store; Milky Way, Reese's, M&Ms, everything; and set out for Kay's party.

Semicolons set off independent clauses - what would otherwise be complete sentences. Em dashes create breaks in the flow of the sentence; commas are more similar.