If you discover something in elite dangerous, does everyone see it on their map or only you?
I have recently found a planet that was not on my map, however once it appeared, it shows as first discovered by ######.
So that implies that others can discover things while it is still not known by all.
Can anyone explain the mechanics behind this?
It is a little complicated. Everyone starts with the same galactic database. There are well known systems everyone can see all the details of. There are purchasable systems where you can buy the exploration data and there are unknown systems where you can't even buy the data. This selection does not appear to change - so for example lots of people have been to Sag A*, but the system isn't purchasable.
When you visit a purchasable system or unexplored system then you need to use the system scanner (basic, intermediate or advanced) to find any of the other astronomical bodies in the system. Once you do you'll be able to see lots of information about them, including first discovered tags. Confusingly there is a bug so some purchasable and unexplored systems don't have tags on bodies, but these have actually been discovered already.
In order to be eligible for first discovered status you need to scan the unknown object with a detailed surface scanner. First discovered tags are only awarded once you
sell the data to Universal Cartographics. If someone visits the system after you, but sells the data first, they get the credit. Once one person has sold the data the system will show their tag for anyone looking at the system map.