Is there a difference between a SELECT statement inside a transaction and one that is outside of it?

Yes, the one inside the transaction can see changes made by other previous Insert/Update/delete statements in that transaction; a Select statement outside the transaction cannot.

If all you are asking about is what the Isolation Level does, then understand that all Select statements (hey, all statements of any kind) – are in a transaction. The only difference between one that is explicitly in a transaction and one that is standing on its own is that the one that is standing alone starts its transaction immediately before it executes it, and commits or roll back immediately after it executes;

whereas the one that is explicitly in a transaction can (because it has a Begin Transaction statement) can have other statements (inserts/updates/deletes, whatever) occurring within that same transaction, either before or after that Select statement.

So whatever the isolation level is set to, both selects (inside or outside an explicit transaction) will nevertheless be in a transaction which is operating at that isolation level.

Addition:
The following is for SQL Server, but all databases MUST work in the same way. In SQL Server the Query Processor is always in one of 3 Transaction Modes, AutoCommit, Implicit, or Explicit.

• AutoCommit is the default transaction management mode of the SQL Server Database Engine. .. Every Transact-SQL statement is committed or rolled back when it completes. … If a statement completes successfully, it is committed; if it encounters any error, it is rolled back. This is the default, and is the answer to @Alex’s question in the comments.

• In Implicit Transaction mode, “… the SQL Server Database Engine automatically starts a new transaction after the current transaction is committed or rolled back. You do nothing to delineate the start of a transaction; you only commit or roll back each transaction. Implicit transaction mode generates a continuous chain of transactions. …” Note that the italicized snippet is for each transaction, whether it be a single or multiple statement transaction.

• The engine is placed in Explicit Transaction mode when you explicitly initiate a transaction with BEGIN TRANSACTION Statement. Then, every statement is executed within that transaction until you explicitly terminate the transaction (with COMMIT or ROLLBACK) or if a failure occurs that causes the engine to terminate and Rollback.