Many times you will see sports stars, race car drivers, and especially Olympians who have "sponsors". Someone, usually a company, has given them money to help them pay for their effort or overhead - money to maintain the racing team, to pay for the travel costs of athletics, etc. - and so the name, logo or jingle of a product or company appears on their uniform or race car, sometimes even on their bodies. This is sponsorship but is also similar to advertising, and usually has the same purpose. A significant portion of large companies' marketing budgets are set aside for sponsorships.
An endorsement is when you hire the person as sort of a paid pitchman. They star in commercials, public appearances, special events, or commercials with that product, which they say is great. Other times they'll be paid just to wear Hanes t-shirts, or golf with Top Flight golf balls.
The main (and subtle) difference, then is that endorsements are usually payment to the individual, where sponsorships are payments to support the individual or groups cause or efforts.
Are you just asking what these two things are?
Endorsements are when you pay (usually) someone to say that your product is great. Presumably, this is someone that the public either trusts and/or admires.
A sponsorship is when some company pays to help you produce something to defray the costs that you piled up when you built something. Companies used to sponsor TV shows -- they'd pay the costs of producing the shows. They still sponsor things like the Olympics.
So, you can use the sponsorship money to hire people to endorse your product. Or you can use endorsers to convince sponsors that your product is worth supporting. So I guess you could say the two are related in that way.
Clarify your question if you like.
The main relationship between endorsement and sponsorship used by businesses is that both are promotional techniques used for promoting products or image of a firm.
Endorsement refers to the practice of public figure expressing support for the company or its products. Generally it is in the form of advertisements. In this case the company pays the person for endorsing its products.
Sponsorship refers to financial and other form of support extended by a company for some program or activity. For example, a company may sponsor a TV program, a sporting event or a social service activity. In theory a company can sponsor something without getting any promotional benefit. However, the companies general do the sponsoring in return for specific public recognition and other privileges designed to help them in their marketing efforts. Some times the persons involved in conducting a sponsored event may also endorse the products of the sponsors.