The Google+ Photo Upload feature does use your Google Drive storage, but it keeps them in a separate photo-oriented storage view accessible through your Google+ account. You can use the Photos app to view your photos on your phone or go to
https://plus.google.com/photos to see them on your computer.
In the photos app if you go to Settings -> Auto Backup you will see a number of options that determine when and how it will upload. I have mine set up upload on any connection but only when my phone is charging, for example. You can set it up to upload as soon as you take a picture though, or only whenever you're on WiFi if you have a limited data plan.