Turbo tax is asking if my wife had a high deductible plan. Is this a separate plan than mine or if she is covered under my plan?

If the program is asking if your wife had a HDHP, they are asking if she had her own separate plan.

Please see this answer from AnthonyC.

If your spouse was covered under your family HSA plan, see the following:

When going through the questions, you will get to a screen entitled "What type of High Deductible Health Plan did [spouse] have on December 1st 2020?" (see screenshot below).  

If your spouse was covered under your health insurance plan, then you should select "none" not "family or self-only." You are selecting none because your spouse does not have their own coverage, they are covered under your plan.  If you select one of the other options, then you will get the notification about a coverage lapse.