Does SQL Server handle databases on SMB shares different than on Hard Drives?
As far as I know SQL server does nothing extra when using databases on a network share. The network link between it and the machine hosting the share going down would most likely be treated the same way as a disk error: the affected databases would be dropped into a "suspect" state until someone takes restorative action.

Recent improvements in the OS fileshare layer (i.e. in Windows, not SQL Server directly) with the introduction of SMB3.0 and related updates make problems less frequent and less severe though, assuming you are using Windows 2012 on both the SQL box(es) and the one(s) hosting the file share(s). See here and here for some more detailed relevant discussion.