Difference Between a Loudspeaker and a Buzzer

What is the diffenence between a loudspeaker and a buzzer?

Traditionally a buzzer was a device designed to make noise. Traditionally it would have been an electromechanical device. It would typically be supplied with DC and the oscillations would have been produced by an electromechanical process inside the buzzer.

A speaker was/is a device used to reproduce sound from an electric waveform with the sound coming out being at least a passable analogue of the signal going in.

However in more recent years the world has moved on. The relative cost of electronics in general and micro controllers in particular has dropped compared to the cost of electromechanics.

So nowadays instead of a traditional mechanical buzzer we often use "piezo sounders". These are something of a half-way house between the traditional buzzers and speakers. They are driven with an audio-frequency waveform, typically a square wave. That allows multiple tones for different types of alert and even allows playing crude music. However they are not designed to reproduce arbitrary audio with anything like reasonable accuracy.

Whether to class piezo sounders as "buzzers", "speakers" or neither is somewhat a matter of semantics.

I suspect the "mistake" is actually a case of your instructor disagreeing with whoever wrote the course material rather than a real mistake but without more detail it is hard to be sure.