The "months" associated with the scans are based on the time frame in which the date you want to camp falls into, not the amount of time the scan will run. For example, if the date you are aiming to find a campsite is 11 months away, you will need to choose the "12 month turbo scan" to cover scans that far into the future. If you are searching for a date that's in 3 weeks, you can choose the "4 month" scan, but will also have the choices for the other two types, depending on how frequently you want the system to scan for your campsite.
The scan will cease after your date of arrival is at hand. The scan will continue through your arrival date on the campground(s) you have selected, even if it finds something sooner. You can also choose to pause a scan at any point if you'd like to stop receiving the alerts before the official end date of the scan.