Competitive pool swimming recognizes four strokes: freestyle, backstroke, breaststroke, and butterfly. Under World Aquatics rules, freestyle means a swimmer may use any style, which in practice is almost always the front crawl; backstroke is swum on the back; and breaststroke and butterfly both require the arms to move simultaneously, with breaststroke using a frog-style kick and butterfly a dolphin kick.
All four are combined in medley events. In the individual medley each stroke covers one quarter of the distance in the order butterfly, backstroke, breaststroke, freestyle, while the medley relay runs backstroke, breaststroke, butterfly, freestyle, because backstroke must start in the water. During the freestyle leg of a medley, swimmers may not use any of the other three strokes.
Source: World Aquatics Competition Regulations (Part Two: Swimming Rules)
Image: Butterfly stroke, Schwimmschule Steiner, CC BY-SA 4.0, via Wikimedia Commons.