Answer: The iPhone and iPad need to each be backed up separately - backing up one does not back up the other.
You are correct that you can back up your devices by plugging in to your computer - by using iTunes. (I am assuming here that you are plugging in to the computer that you normally sync your devices with.) Just make sure that iTunes starts up and the message at the top shows that the device you have plugged in is backing up (as well as sync'ing) your device.
If it doesn't back up automatically, you can force the backup of the device by right-clicking on the device in the Sidebar, and choosing Backup. (If you don't see a sidebar, you can turn this back on from the View menu.)
The other option is to back up your devices to your iCloud rather than to a computer - something that can happen automatically each day without you having to remember to do it!