What is the correct action for the Research Lab?

1) Action: Draw 1 engineering and 1 tactics Skill card.

OR

2) Action: Draw 1 engineering or 1 tactics Skill card.

We have been playing that you get one or the other card, not both.

The space reads: Action: Draw 1 engineering or 1 tactics Skill card.

Does something contradict this?

Right, one or other, not both.

Even says in the rulebook (page 12):

Example: William Adama is in the “Research Lab” and
uses the action listed there to draw one tactics or one
engineering card. He may choose to draw engineering
even though it is outside his skill set, because the location
specifies the card type

Only way to get both would be to have an Executive Order played on you if you were already in the Research Lab (so you get 2 actions).