Azure webjobs vs scheduler
The actual scheduling bits of WebJobs are built on top of the scheduler. When you set up a Web Job on a schedule under the hood it uses the scheduler to kick it off. WebJobs provides a nice little location to host the code that gets executed. In fact, if you create WebJobs for a web site look in the Scheduler on the portal and you'll see them listed there as well.
Also note that the scheduler could call out to other systems not running Azure. If you have something running in a Cloud Service that needs to be called regularly, or even if something was hosted elsewhere (another provider or on premises) the scheduler is where you can set that up.
Regarding the cost aspect, there is a free tier to the scheduler as well: http://www.windowsazure.com/en-us/pricing/details/scheduler/.
It's 2016. The below answers are no longer accurate.
WebJobs now also has a built-in scheduler and the schedule can be defined by a cron expression.
When publishing to Azure, you can choose if you want to have the WebJob sparked off by the Scheduler or by the WebJob internal scheduler.
Important Note: The Azure Scheduler has limits to frequency of either 1hr or 1min depending on if paid or not. For the internal scheduler however, your App Service requires Always On to keep on running and firing off the job. This Always On status may affect your pricing.
Continuous jobs are monitored, and if they exit they are re-executed. In this way they act more like "services" in your local machine. There is a module that monitors and keeps your app working. Always-ON is a feature that will help your site stay alive and hence, your webjobs to continuously run.
Scheduler is used to trigger the webjobs. It uses the scheduler user account (not the back-end account). This way you can move out of the free tier for scheduler, sign up to higher tiers to suit your needs. But essentially, all the scheduler is doing is hitting an https endpoint (which is public, but required your auth).
Triggered jobs (scheduled and on demand) are invoked by an https call. These calls are load balanced - much in the same way that a web app with many instances is load balanced. Continuous jobs run concurrently by default, but can be set to be a singleton.