Patient ... you have it spot on, but a couple number examples to clarify it if anyone else comes into this thread.

Attack/Save: Attack Roll

Player Attack Roll: Proficiency (2) + Strength or Dex (2) = +4.
Enemy Defense of 16.
The PLAYER makes a roll (1d20+4) to beat this target (16).
So the result has to be 12 or higher on the d20 to hit (12 + 4 = 16)

Attack/Save: Dexterity

Target Dexterity (2) + Proficiency (2) = +4
Spell Save is 8 (base) + Proficiency (2) + Intelligence (3) = 13
So the TARGET makes a roll of (1d20+4) to beat this target (13).
For the target to avoid / reduce the effect, they'd have to roll 9 or higher on the d20 (9 + 4 = 13)


Figured seeing it written out in detail may also help.