The manager is considered the account manager – the contact person for the client. The manager field is automatically prepopulated with the manager from the client's record when you select the client's name on the job, but can be changed afterwards.
The owner is the project manager – the person responsible for completing the job. The guy holding the whip, chasing after everyone who has tasks to complete on that job, so to speak. You can assign multiple project managers by holding down the ALT key or even everyone by pressing the ALL button (used mainly for internal jobs).
Many companies don't distinguish between the owner and the manager, while for others – particularly in larger teams – the distinction is more relevant.
In the jobs list, you can call to see "My Active" jobs, which finds all jobs where you are the owner. If you wish to see all active jobs where you are the account manager, you can go to the Jobs menu and select "Show my active jobs (As account manager)".