As you have probably guessed, the main factor in determining what type of rope to buy depends on what you will be using it for. Between trad climbing, sport climbing, top rope climbing, ice climbing, or mountaineering there are several different kinds of ropes or rope features that have different ideals for each sport. Here are some of the basic differences between ropes, and what type of climbing you may need them for:
Single Rope: Best for trad, sport, and top rope climbing. The name single indicates that the rope in meant to be used by itself, and not in coordination with other ropes (such as twin ropes).
Half Rope: Best for trad climbing, on wandering routes, mountaineering and ice climbing. Half ropes reduce the amount of rope drag on wandering routes, and overhangs. Half ropes also provide redundancy in the event that one rope is damaged during the climb. Half ropes are always meant to be used in twos, clipping to your left and right while ascending.
Twin Rope: Best for trad climbing on non-wandering multi-pitch rock routes, mountaineering and ice climbing. Twin ropes are another two rope system, however you always clip both ropes through the same clip, unlike the half rope system. These ropes also provide redundancy in the event that one rope is damaged.
Static Rope: Best for rescues, climbing fixed lines with ascenders and hauling loads. Static ropes excel in situations where you don’t want the rope to stretch, such as when you are lowering an injured climber, ascending a rope, or hauling a load up with the rope. You should never lead or top rope with a static line.
Dry Treated Rope: Dry treating a rope provides moisture protection, which can prevent the rope from becoming heavier, and less able to withstand falls. Dry treated ropes are more expensive, and often not necessary in most top rope, or sport climbing situations.
For more information on rope types, here are two great articles that offer more details about each kind of rope, as well as differences in diameter, rating, and more. These articles are what we used to educate ourselves for both this article, as well as to make our own rope buying decisions. If you have any other articles that provide good information of the differences between ropes, or how to pick a rope, feel free to leave a link to it in the comments!
https://www.rei.com/learn/expert-advice/ropes.html
https://www.mec.ca/en/explore/about-climbing-ropes