There are two ways you can get Piwigo. Either you host it yourself, for example with OVH or BlueHost, In both cases you keep your full data ownership.
Run Piwigo on your own web hosting, providing PHP and a MySQL database. There is no cost for Piwigo itself but you'll need to update Piwigo when new releases are available to keep it secure and fast.
Forget technical tasks if you decide to go with Piwigo.com. Install, updates, backups are fully managed on a dedicated infrastructure, tailored for Piwigo. You will also get dedicated support from the makers of Piwigo.