How is pasteurization different from sterilization?

Basically, pasteurization is a process that kills most bacteria. Sous vide is a method that you can use to pasteurize food (eggs for example) which will kill most, but not all, bacteria. Sterilization is a method of killing all bacteria (e.g. by irradiation or heat). Sterilization would be what you'd want to use for canning, for example.

Milk is pasteurized by the manufacturer and can use lower heat for a longer period or higher heat for a shorter period.

Although yes, pasteurization is not as complete as sterilization, there's one subtle difference that's not been mentioned in the other answers: pasteurization is always a heat treatment done to something that can spoil.

Sterilization, on the other hand, can be done on things that can't spoil, such containers, utensils, or preparation surfaces (cutting boards). As such, it isn't always a heat treatment, and may be a chemical or radiation treatment ... although they're not going to be as common in home kitchens.

Must home cooks will "disinfect" rather than "sterilize", which like the distinction for pasteurization, is about reducing the harmful pathogens, not about removing them completely like sterilization.

They are not the same.

Pasteurization is the use of high temperature (think 100C max, though lower temps are typical) for a short time (HTST) in order to destroy pathogens and increase shelf life. Pasteurization does not kill or deactivate all microorganisms, but drastically reduces the bacterial load.

Sterilization is a process that is used to stop ALL pathogens and renders a product shelf stable. It requires temperatures above 100C.

The difference between the words has mostly historical roots. Both refer to a process which reduces the number of bacteria. The important difference is the proportion of bacteria killed. Contrary to popular belief, sterilization doesn't kill all bacteria.

Microbiologists measure bacterial reduction in log numbers. There are different levels of sterilization possible, but many common processes are standardized to ensure a log 6 reduction, this means that only one bacterium per million will survive sterilization. So it is not exactly correct that all bacteria will be killed, although for everyday food storage, it is a close enough assumption.

Pasteurization is done at reduction levels that are lower than sterilization. Again, different levels are possible, but the standard process for milk is designed to reach a log 5 reduction, or 1 bacterium in 100 000.

Don't be fooled by the apparent small difference between 5 and 6, or even by the factor of "only" ten - you can see the difference in milk, where sterilized milk stays germ-free for years in an unopened container while pasteurized milk would spoil pretty soon if you left it (in the sealed container) at room temperature.

I am using milk as the example, as it is the most prototypical one. But you will find that many other foods are pasteurized, for example fruit juice or beer. Also, the word seems to only have established itself in the context of preparing liquid food for selling, plus a few other rare uses such as pasteurizing egg yolks for mayonnaise at home. In principle, cooking a stew at home likely also achieves a log 5 reduction in bacteria, but it would be very weird to refer to it as "pasteurization".

Sterilization is the overall name given to processes which should kill all biological pathogens (e.g. by irradiation or heat). Sterilization would be what you'd want to use for long term storage via canning for example. Biological pathogens, would include molds, viruses, and bacteria.

Pasteurization is a particular sterilization done on milk and milk products primarily. Pasteurization kills most of the biological pathogens but not all. If milk is heated to a high enough temperature to kill all the biological pathogens then the sugars in the milk caramelize and the milk develops an off taste.