Coagulate, congeal, set, curdle, clot, jelly, jell are comparable when meaning to form or cause to form a stiff mass that is solid or at least cohesive.
Coagulate implies a thickening or solidification of a liquid and usually the making insoluble (as by chemical reaction) of something that was soluble.
Congeal specifically implies a thickening or solidification by means of cold; the mass thus affected may dissolve or become liquid when the temperature rises again.
Set (see also SET) carries no implication of how the stiffening, or making solid or viscid, occurs but only of the nature of the effect.
Curdle basically implies the coagulation of milk (as through souring or the addition of rennet) into a soft but solid part (the curd) from which cheese is made, and the separation of this part from the watery part (the whey); in more general use the term connotes a thickening and sometimes a souring.
Clot implies the coagulation or congealing of a liquid into lumps or masses or, less often, the gathering of something light and diffuse into hard accumulations or lumps.
Jelly specifically implies the setting during cooling of a cooked liquid (as broth or juice of meats) containing gelatin from animal tissue or one (as fruit juice and sugar) containing the pectin of acid fruits.
Jell is basically identical to jelly, but unlike the latter it is often used especially in negative constructions to imply the state when nonmaterial things (as ideas or plans) attain fixity or cohesiveness.