...if you have a card that says "draw a card, you can't this turn from your deck. usually no one can either the cards say "no heroes can draw extra cards"
^Pretty much this.
The “can’t draw extra cards” clause applies to cards that would be drawn as the result of a card effect and/or a villain reward. This includes cards that would be drawn because another player played a card that told you to draw a card.
Spoiler (click to reveal)
This also includes cards that would be drawn as the result of the “card” icon coming up on a die roll, and cards that would be drawn through the activation or triggering of a proficiency.
The active player still draws a new hand of cards at the end of the turn, since these are not “extra” cards.