Spot instances and on-demand instances are two separate systems. While on-demand systems are available all of the time, you set a maximum bid for spot instances instead. If there are systems available for that price, they will be launched. However if there is a higher demand in your availability zone, these systems may be terminated without notice. So for hosting a website on AWS, I would not recommend using spot instances. If you want to reduce the price, you can have a look at reserved instances instead.
That said, you would probably have to stop your on-demand machine and set up a spot instance request for this machine instead.