I feel that one of the terms that should be banned is "snapshot backup." The term "backup" implies that as long as you have the backup file, you'll be able to restore the DB to the point it was at when the backup was made. With snapshots, this may NOT be the case.
This is because the snapshot contains only the unaltered data pages than have been altered in the database file since the snapshot was created. The advantage of this is that snapshots are fast to create and may be faster to restore than full backups, but if you lose the database file (such as from a hard drive failure) then the snapshot is useless.
Also, if you are doing massive changes to a database you intend to undo with a snaopshot restore, and the I/O cannot keep up, you may end up with snapshot than cannot be restored. This happened to me last year when I made a snapshot to a 500GB DB before deleting most of the data, running a SRINKFILE, an upgrade form the software vendor, a backup to create a new version of the database, then tried to restore it using the snapshot. I thought I was saving a couple hours by not running a full backup first, but it turned out that the snapshot had been corrupted from an I/O error and could not be used. If I made a full backup prior to making the major changes I would have been fine.
Snapshots will not affect the backup chain. However, you must drop any existing snapshots before restoring from a fulll backup.