I'm confused. Do I need both: Basic scanner AND advanced discovery scanner?
NO.
You -have to have- one of: Basic Discover Scanner - Improved Discovery Scanner - Advanced Discovery Scanner
When triggered, those will pulse and add all celestials within 500 / 1000 / infinity lightseconds to your nav tab as 'unexplored' and allow you to target them to get a detailed scan. Also, if you ahve any of these on your ship, you will automatically add to yoru nav tab any bodies you approach within a certain radius as 'unexplored'. This is why the main star of the system shows up on your list a few seconds after you arrive - your discovery scanner adds them because they're close. If you have NO discovery scanner (basic / improved / advanced) then this first star will never get added to your nav tab, and you will not be able to add any bodies to your scanner so you cannot target them to get a detailed scan.
All ships have a 'basic scanner' on them; this has no slot and is on all ships and is unchangeable. It will let you target a body that is 'unexplored' and get basic information - star type, planet type, etc., and get you more cash.
You can also add a 'detailed surface scanner', which takes up an internal slot. If you have one of those on your ship, when you target an 'unexplored' body and complete the scan you get more information - star temperature, atmosphere and planetary composition, etc. This increases the payout you get for having scanned tehse bodies.