User blog comment:Omega natsu2/Chapter 369: The Place Prayers Reach, Predictions./@comment-31.132.65.50-20140129025714/@comment-7418318-20140129171155

Both in the manga and the anime "Siegrain" touched Erza at the chin and lifted her head a bit to look directly into her eyes, so it is possible to create a thought projection that can physically interact like a real body.

And from Jose we know that it's possible to create TPs that are just an image. So both kinds are possible.

Considering how weakened Jellal was, while Siegrain existed, my guess is that it takes a lot of magic power (as in a constant drain, not just a one-time investment) to maintain a Thought Projection with a physical form.