What George said. I just wanted to add that:
Theoretically, you can indeed restore SQL Server from Windows Server Backup. (You would detach the old database, rename the old files, put the .mdf and .ldf back in the right places and use the attach feature.) It's not generally recommended, however (unless you've had some horrible disaster that took out your actual SQL backups). This is because uncommitted transactions might not be on disk yet, and also because log backups do some additional housekeeping for databases in Full Recovery.
How Bad [TM] this is depends on your database. If your database is basically the brains of a piece of commercial software that you never interact with on a SQL level, this is considerably Less Bad than if your database is used for banking or financial data with a high transaction volume, for example.
Personally, even when using SQL Express or Windows Internal Database I back up with actual SQL backups rather than relying on Windows Server Backup. (I use task scheduler to kick off Ola Hallengren's scripts with SQLCMD.)
(In my opinion, there's nothing wrong with the built-in SQL Server backup commands. Many people find commercial GUIs or other people's scripts easier to use, however.)