A full backup includes databases and other items as well as your files on the server. It must be restored by support. A backup of the home directory should include everything as you stated, but does not have the databases which must be backed up separately.

You should regularly make your own backups and store them locally, not on the server. Although LP advises they backup daily, I have seen them loose an entire site (actually an entire server), on  which they could not restore any customer data. They simply advised ALL the backups were corrupted. Customers that did not have backups of one sort or another had no recourse but to start over from scratch.