Say I have two tables (Apples and Oranges) with the same columns and just a different table name. Would there be any advantages/disadvantages to turning this into one table
Depends on constraints:
apples that don't exist on oranges (or vice-versa)?apple can have the same ID as some orange)?If the answers on these two questions are: "yes" and "no", keep the tables separate (so constraints can be made table-specific1).
If the answers are: "no" and "yes", merge them together (so you can crate a key that spans both).
If the answers are: "yes" and "yes", consider emulating inheritance2:

1 Lookup data is a typical example of tables that look similar, yet must be kept separate so FKs can be kept separate.
2 Specifically, this is the "all classes in separate tables" strategy for representing inheritance (aka. category, subclassing, subtyping, generalization hierarchy etc.). You might want to take a look at this post for more info.