Like any mobile phone, you can turn a smart phone off (to save battery).
If you leave the phone turned on, but not actually using it (e.g. so the screen goes off), the battery drain is pretty low and will last quite a while (you'd have to look at individual phone specs for details of standby times).
The biggest drain on a smartphone is anything that keeps the screen active. So watching movie or music videos can be a big hit.
All the above also applies to a tablet.