what is the difference between thick and liquidy cupcake batters?

This is a pretty general question, and there are a lot of different methods and ingredients that can affect the thickness of cake batter and the density of cakes or cupcakes.

Most cupcake batter is really just regular cake batter cooked in smaller amounts. Although there are sometimes different instructions for how to do fancy tricks like filled cupcakes, the actual batter itself is usually the same batter as used for the various other cakes like plain yellow sponge cake, carrot cake, chocolate cake, etc. There are a lot of different styles of cakes and, with very few adjustments, most of them can be made into cupcakes.

Usually the thicker batter will form a denser cake (and thus, a denser cupcake). It may have more egg and/or use butter instead of oil, and may have heavier additional ingredients like fruit (apples, bananas, pumpkin, shredded carrots) or a lot of chocolate, and/or nuts mixed in. If you were making this as a cake instead of a cupcake, you'd probably be more likely to make a quick bread loaf or perhaps a bundt cake or a sheet cake -- it's less likely to be a layer cake.

A thinner batter will generally form a lighter, fluffier cake (or cupcake), the kind of recipe that would work well as a layer cake (or a sheet cake). It may use oil instead of butter, and it may have steps such as separating the egg yolk from white and whipping the egg whites. It probably doesn't have a lot of heavy ingredients that would tend to sink to the bottom through the light batter.