I noticed … then remembered … that Pathfinder has close ties to D&D, right ?
So, I thought, knowledge of (A)D&D would make things easier …
However, I wonder, what is different between both, mechanics-wise ?
Yes, Pathfinder branched out of D&D 3.5E, the first edition is a modification of it. They're not much different but Pathfinder didn't follow all the modification that D&D received in 4th and 5th editions. (there is a Pathfinder 2E too, but Owlcat Games are using the 1st)
Pathfinder has a more complicated description of the rules, it's specified in more details than D&D. D&D leaves much more up to the DM to decide.
I think that 5E differs mostly with penalties when the character is not proficient with armours and weapons. The different types of actions are organized differently (action, bonus action, reactions, interactions), maybe there Pathfinder is a bit simpler.
They've also introduced concentration in D&D, so that your wizard or your cleric can only maintain one concentration spell active at any moment: if a cleric casts
bless, he cannot spawn
spiritual weapon without ending
bless. Not all spells require to maintain concentration, some of them can still be cast without interrupting
bless, for ex.
EDIT: Oh, and 5E has the advantage / disadvantage system, it wasn't there in 3.5, I don't know about 4E. Pathfinder is not using that.