We investigate the kinetics of spreading and adhesion between polymer vesicles decorated with avidin and biotin, held in micropipettes to maintain fixed tension and suppress membrane bending fluctuations. In this study, the density of avidin (actually Neutravidin) and biotin was varied, but was always sufficiently high so that lateral diffusion in the membrane was unimportant to the adhesive mechanism or rate. For a stunning result, we report a concentration-dependent distinction between adhesion and spreading: At low surface densities of avidin and biotin, irreversible vesicle adhesion is strong enough to break the membrane when vesicle separation is attempted, yet there is no spreading or "wetting". By this we mean that there is no development of an adhesion plaque beyond the initial radius of contact and there is no development of a meaningful contact angle. Conversely, at 30% functionalization and greater, membrane adhesion is manifest through a spreading process in which the vesicle held at lower tension partially engulfs the second vesicle, and the adhesion plaque grows, as does the contact angle. Generally, when spreading occurs, it starts abruptly, following a latent contact period whose duration decreases with increasing membrane functionality. A nucleation-type rate law describes the latency period, determined by competition between bending and sticking energy. The significance of this result is that, not only are membrane mechanics important to the development of adhesion in membranes of nanometer-scale thickness, mechanics can dominate and even mask adhesive features such as contact angle. This renders contact angle analyses inappropriate for some systems. The results also suggest that there exist large regions of parameter space where adhesive polymeric vesicles will behave qualitatively differently from their phospholipid counterparts. This motivates different strategies to design polymeric vesicles for applications such as targeted drug delivery and biomimetic scavengers.