Upvote:1
The confusion you have might be connected with the different modes of transportation.
Indeed while travelling to the US by land from Canada does not require you to get an ESTA, it does not absolve you from having to get a visa or instead be eligible for the VWP. Remember ESTA and VWP are not the same thing, the difference is explained in other answers pretty well.
If you fly to the US, you would still need to get an ESTA. Some exceptions may apply, you can check at the CBP website. As you correctly assumed, this requirement does not apply to Canadian citizens.
I have no idea how this is connected with your status in the US, though. This may be explained in the question linked to in the comment by Michael Hampton.