As you know, the human hearing range is about 20Hz to 20000Hz. There is no single speaker could cover the full frequency range.
Tweeter: The name was originally from the word tweet and it represents some birds' high pitch sound. Tweeter is the smallest type compare with others, the size is small, but it cover treble range about 3K to 20K Hz.
Mid-Range: The speaker size is about 65mm to 100mm, it could cover from 250 Hz to 2000 Hz frequency range. It handles the most important human voice.
Woofer: The speaker size is about 160mm ~234mm with the huge magnet in the bottom. With the larger cone and magnet motor, it represents the low frequency at 60Hz to 2000Hz.
Full-Range: As you could see from the name, it will cover a bigger frequency range from 200Hz to 5000 Hz. In the car speaker, it was most applicable in the read door woofer. So it is needs to be improved in the high frequency performance, there is a hore or whizzer in the center of cone.
Coaxial: The design is similar with woofer, but there is an additional tweeter sit in the center of
speaker, it could provide much more high-frequency coverage.
Subwoofer: The speaker size starts with 200mm+ and most with double Voice coil or magnet, it provides the powerful motor to present the up-down human hearing at 20Hz to 200 Hz frequency range. In-car subwoofer, some the core speaker is designed sit in an enclosure. The enclosure could be made by plastic or wood.