The two families
Almost every drone you will meet is either a multirotor or a fixed wing. A multirotor generates all of its lift with spinning propellers, so it can take off vertically, hover in one spot, and fly in any direction. That flexibility costs energy: the motors never stop working against gravity, which is why most multirotor flight times land between 10 and 30 minutes.
A fixed wing gets its lift from a wing moving through the air. It cannot hover, and it needs space to launch and land, but it covers far more ground per battery. That makes fixed wings the standard choice for mapping, survey, and long-endurance work. VTOL hybrids try to get both: rotors for takeoff and landing, a wing for cruise, at the cost of complexity and weight.
Size classes
Frame classes are usually named by wheelbase, the diagonal distance between motors in millimeters. An F450 has a 450 mm wheelbase. Small quads are often named by propeller size instead: a 5-inch freestyle quad, a 7-inch long-range quad, a 65 mm tinywhoop.
Size drives everything downstream. It sets prop size, which sets motor KV, which sets battery cell count. A 5-inch quad on 6S is a completely different aircraft from a 3-inch on 4S even though the parts look similar in a photo.
Purpose-built shapes
Cinewhoops are small ducted quads meant to fly safely near people and objects while carrying a camera. Tinywhoops are their indoor cousins, light enough to bounce off a wall without damage. Racing quads strip everything that is not speed. Camera drones (the folding consumer kind) prioritize stabilized footage, obstacle sensing, and ease of use over agility.
Heavy-lift multirotors with six or eight motors exist for payload and redundancy: losing one motor on an octocopter is survivable, while losing one on a quad usually is not.