Why does my iPad storage say photos-14.3 GB when I only have 30 min of footage?

Not sure why both other replies here are about the "Other" category in Storage, when the question specifically asked about "Photos".

However - a member of my family had exactly the same issue: 7.7GB of iPad storage taken up by Photos despite having only 400 photos on her device, and iCloud Photos correctly activated.

We eventually worked out that the problem was with Shared Albums - she had accepted an invite to a Shared Album containing 3,500 photos and 465 videos. When we Unsubscribed from that album, the Photos storage usage dropped from 7.7GB to 0.5 GB

Like many people I always assumed that the on-device storage consumption of Shared Albums would be configured to be absolutely negligible - this example shows that in the case of very large Shared Albums, that may not be the case.

Apple is notably silent on this issue in all official Support articles and responses on forums like this one.

The 'Other' storage on your iPhone are files which do not fall into clearer category labels like applications, audio, movies, photos, etc. This is the space taken up by text messages, emails, documents, and etc. It is also where data from apps are stored; things like settings, it's web cache, etc. 

These files are not harmful to your device but if they accumulate too much space, over time it can blow up your storage space. All these things are backed up when you back-up the phone, which is why it's still there when you restore from a back-up. 

Here are some solutions you can follow to optimize your iPhone storage: 

1. Make sure your phone and apps are synced in iTunes. 
2. If possible, make sure you have backed up or copied off any documents or data you might need, as you will lose it. A lot of apps allow you to email documents and data. 
3. On the phone, go to Settings > General > iPhone Storage. You should find a list of all the apps. The list is mainly 3rd party apps, not apps that come with the phone. 
4. On the right hand side, is a list of the total storage space the app is using including the app itself. The list is also handily listed in descending order of size. If you tap on on one of the apps on the list, it shows you how much space is being used by documents and data. You also have the option to delete the app. 
5. To delete the app, simply tap on Delete App. The app is deleted, and so is the data which is stored in the 'other' area. Repeat for other apps if necessary. 
6. To re-install the app(s), plug it in to your iTunes and re-sync your phone. The app(s) are re-installed with no data taken up in the 'Other' area. 

Hope it helps!