Not necessarily. The design of the lens elements are essentially the same, either way. The only common difference is the Petzval used for cameras will usually have some kind of aperture control.
Of course, "Petzval" is kind of a generic term used to describe a certain general formula of a lens that contains two specific types of doublets. How exactly that's implemented, can vary from manufacturer to manufacturer, so they're not all identical. So it's possible that two specific Petzval camera lenses can be even more dissimilar than a specific Petzval camera lens and a specific Petzval projection lens.
Now, it's not unheard of for people to pass of other lenses that exhibit spherical aberrations as Petzval lenses. For instance, I once owned an f/0.9 projection lens that had some pretty severe spherical aberration. It also had something like 10 elements, so it was clearly not a real Petzval, though I had seen that same type of lens sold under the name "Petzval" before by some unscrupulous sellers on the internet.