There are a few different types of grease used in automobiles, and there are many different ways they are applied. Some greases are thick and are either applied by hand or with a grease gun, while others are thin enough to be sprayed from an aerosol can. Greases tend to be thicker lubricants than and others used on vehicles.
High Temperature Grease
High temp grease is used for any high temperature application where normal grease would be degraded or liquefied by heat. This is sometimes needed to lubricate engine mounts which are close to exhaust components, and sometimes substituted for any standard grease in racing applications.
When in doubt about if a component will ever get too hot for standard grease, high temp should be used; you never know what unusual circumstances may heat that component up more than usual, or how off your estimate may be.
Synthetic grease is a general upgrade from standard grease. It lasts longer, can withstand a bit more heat, lubricates a little better, and resists water much better (it is often waterproof).
White Lithium Grease
White lithium grease is commonly used for low-demand lubrication, such as door hinges and pedals. It is often sold in aerosol cans, but can also be bought in a tube for more precise application. It is much more thin than most other automotive greases.
Dielectric grease also goes by silicone grease or bulb grease, and is often used to seal electrical connections. It is quite weatherproof, and good at sealing components.