thank you for your question. Both apps are officially support by us.
The ownCloud Online app is free because it is included in a subscription for our SaaS cloud solution ownCloud Online (https://owncloud.online). It also works only with ownCloud Online servers.
The “normal” app can be used for any ownCloud server, hosted, managed, on-premises or whatever else.
I hope I could clarify things. If you have additional questions feel free to contact me any time.