Present continuous marks permanent facts, while present simple marks actions in progress, which makes teaches describe a current action and is teaching describe a permanent schedule.

Present simple is used for actions happening at the moment of speaking, while present continuous expresses habits, which makes teaches refer to what happens now and is teaching refer to routine.

Both forms are interchangeable in classroom English, and the difference is mainly stylistic, so teachers can treat teaches and is teaching as equivalent in meaning.

Present simple typically expresses routine or repeated actions, while present continuous highlights a temporary or currently developing situation, matching Mondays as routine and this week as temporary.

Present continuous is preferred for teaching verbs, so is teaching fits routine and teaches fits emphasis, because continuous carries the neutral form in modern textbooks.