Do all triangles sound the same note in the same octave, or are there differences between models?
There are many differences, both in pitch and timbre. I've seen triangles used with a 10" side length down to 4", and you can purchase them made out of a variety of different materials and construction methods.
Some pieces even call for three different triangles of different pitch. So no, there's no defined standard pitch. A percussionist just chooses the triangle that he finds most appropriate for the style of the piece (which the conductor may override if he/she feels differently).
Not only that, but orchestral percussionists will carry around a set of triangle beaters of different sizes and weights to further fine-tune the tone of the triangle.