Why is there a storage space discrepancy when I update my iPad locally vs on my PC?

You should aim to maintain at least 4-6GB of available free space for iPadOS to use for temporary storage.

This is particularly important when performing an OTA system software update - as there must be adequate free-space in which to download, unpack and verify an update prior to installation. As soon as the update has been successfully installed, the OS will automatically clean-up temporary files - releasing this space to the system as free-space. Major version updates require considerably more temporary space than smaller point-updates.

If instead using a Windows PC or Mac computer to perform the update, the iPad requires less free-space - and the update package is downloaded, unpacked and verified by the computer. Once verified, the update is applied to the iPad.

If your iPad is capable of update to a more recent version of iOS/iPadOS than is currently installed, these support pages outline both the available methods by which the update can be performed - and troubleshooting should you experience difficulties:

Update your iPhone, iPad or iPod touch – Apple Support

If you can't update or restore your iPhone, iPad or iPod touch – Apple Support

If your iPhone, iPad or iPod touch won’t update - Apple Support

iOS update and restore errors – Apple Support

Be aware that while an iPad may be capable of update, in some circumstances you may need to use a computer to perform the update*. To do so, you will need access to either a Windows PC (with iTunes for Windows installed - or the more recent Apple Devices App) or a Mac (with iTunes or Finder - as appropriate for the installed version of MacOS). Ensure that your installed version of iTunes has been updated to the most recent version; the essential device drivers are included.

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Update software on iPhone, iPad or iPod touch in iTunes on PC - Apple Support

Update your iPhone, iPad, or iPod touch with the Finder - Apple Support

Apple Devices App (Windows PC):

https://apps.microsoft.com/detail/9np83lwlpz9k?hl=en-ms&gl=MS

(*) If you don’t have access to a suitable computer of your own, that of a helpful friend or family member will suffice. Alternatively, the technicians at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP) will be delighted to assist.

Genius Bar Reservation and Apple Support Options - Apple

If you have a beta profile installed, ensure this has been removed from your iPad - as, otherwise, installation of production software updates may be inhibited. This support page provides the necessary information to remove the beta from your iPad:

How to uninstall iOS beta software - Apple Support

You should note that for your iPad to install an available update, its battery must be charged to at least 50% capacity - and/or be connected to its Power Adapter. Similarly, the iPad can only be updated over a standard WiFi connection - or be updated by a PC or Mac using iTunes or Finder - over a USB connection.

No. 800MB is the compressed space. When decompressed and installed it may use up more spaxce, but its unlikely to be 7GB.

When you download it on a computer it is the complete package for all devices which is 7GB, but will only use a portion of that to actually install on a device, so its going to be less than 7GB when installed but still more than 800MB.

The download size, has very little to do with the actual space the update will take up once installed.

Because the download on the device itself gets tailored to the specific device model and version it is running so only downloads the necessary files for the device, while the download through iTunes or the Devices app on a PC is the complete package for all Apple devices and only when it is unpacked does it determine what device its going to be installed on and use that section of the installer for it.

Why it works this way is unknown, however, and we cannot speculate on that here.