Client is a business who`s buying services from freelancers to perform/finish their projects/jobs. You can also edit your account to represent the company you're working for and not as an individual.
An agency is a business that sells the services of multiple freelancers on Upwork. We've created a guide to agencies to help you decide if an agency is right for you. You can also check out this Help Article to learn more about agencies.
If you have any additional questions fell free to post them here.