# non-isotopic but homotopic tight contact structure

By a theorem of Eliashberg, two overtwisted contact structures on a 3-manifold which belong to the same homotopy class (as plane fields), are also isotopic (through contact structures). Is there an example known of two non-isotopic but homotopic tight contact structures on a contact 3-manifold?

Yes, there are known examples. See for example Corollary 1.3C of this paper of Eliashberg and Polterovich for an infinite sequence of examples on $T^3$. There is also a short paper of Akbulut and Matveyev giving examples on homology spheres. There may also be other examples known from the classification results of Giroux and Honda.