The traditional types all work to collect visible light from the sky. Recent types may work outside the visible spectrum. They all have their different advantages and disadvantages and they are used in different areas of astronomy.
Optical
Refractors
Dioptrics.
Telescopes which create their image with an objective that is a convex lens (refractors) are said to be "dioptric" telescopes.
Achromatic: uses convex and concave lenses together, to correct for chromatic aberration.
Apochromatic: a more complex arrangement, for even less chromatic aberration.