if, in ftp , you see public_html then in there you see all the phpBB folders like adm, assets, etc. and, you don't have anything else like a wordpress blog or whatever in your public_html directory, then yes, you download all of the files/folders in your public_html directory to your computer.
and yes, you do the backup from the admin panel.
if your board is phpbb 3.2 or 3.3 then the database backup will go into the folder named store automatically.
therefore, after you do the database backup and the download all the phpbb files/folders you will already have your database backup.
now, not sure why you ask about restoring it unless you have lost it for some reason or you are moving to a new host etc.
the point of a backup is just in case something happens you can then restore everything with just a few clicks.
I'm baaaaaccckkkk. still doing work on donation basis. PM your needs.
Premium phpBB 3.3 Styles
If nobody is in the forest, does a tree really fall?