Lease agreements and service contracts describe two different things. The former is the owner of a physical asset agreeing to let someone else use it in exchange for a fee; the latter is someone with a skill agreeing to use that skill for someone else in exchange for a fee.
Leases refer to real estate like houses, apartments, offices and factories, but they can also refer to equipment like cars, trucks and computers. Basically, they can refer to anything that one person owns that another person wants to use. You could theoretically lease someone a paper towel, toaster or cup if they were prepared to pay your monthly fees.
Where a lease refers assets, service contracts refer to services. In this case, one person pays another person to perform a service for them--carpenters, plumbers, caterers and IT professionals are just a few examples of service contract workers.
Where a lease is very clear because it is a physical asset, a service contract is a little different. If you lease a computer for 12 months, the owner just needs to give you the computer and collect his payments. However, if you contract someone to service your computer for 12 months, you need to make sure you define everything--what service he is providing, what criteria his service quality will be judged by and when it needs to be done. This is because you need to assign tangible qualities to intangible service.