ATK affect basic attacks and elemental skill/ elemental burst that ask you ATK. Physical damage only affect basic attacks and basic attacks modifier. Can affect elemental reaction that requite ATK.
Elemantal DMG affect the portion of the damage that get element. If you have a char that embue the element to basic attacks, the DMG bonus will apply there as well. Mona basic attacks are Hydro, so Hydro Bonus not only will boost her skill/burst, but her elemental attack because have element.
Elemental DMG don't work with melee physical damage, unless you embue with elemental propriety.
I highly recommend read the skill information before make a build. Some skills and heal require ATK or Elemental Bonus.
I get the idea now, thanks. I was just a bit confused because this game doesn’t strictly have physical and special statsCatalyst even more than physical weapon characters want to get the corresponding element damage goblets due to diminishing returns of the ATK stat. Also, artifact Goblet and character passives are the only places you can currently get elemental type damage. The way the damage formula works, it's almost always the best option unless it's a character that has secondary scaling off of attack for something in their kit. An example would be Jean or Qiqi that have their healing scale off of the ATK stat. If you're using them for healers, an ATK goblet would be a better fit than an elemental damage goblet. Even then though, there is still diminishing returns and overhealing, so some people will still run elemental damage or Elemental Mastery instead.