It certainly is true that practitioners using the variety of approaches represented in this discussion use different vocabularies to describe the same concepts. However, I don't think that means we do the same things during sessions or that the client's experience is the same independent of the therapist's approach.
First of all, there are the obvious differences. In Cognitive Therapy (and a number of other approaches) we do things such as starting with an initial evaluation, talking explicitly about the goals of therapy, starting each session by agreeing on an agenda for the session, focusing on specific here-and-now situations rather than talking about issues in general terms, and coming up with explicit "homework" for the client between sessions. We do these things because we believe that they increase the effectiveness and efficiency of therapy. Back when I learned psychodynamic and client-centered therapy, I was taught that one should definitely not do such things. I find it hard to believe that these differences have little impact on the client's experience (or on the outcome of therapy).
Even if we set the obvious differences aside, the therapist takes an active, directive role in CT (and in many of the more short-term therapies) which is quite different from the therapist's role in more traditional therapies. I'm sure that this has a significant impact on the client's experience. First, when I see clients who have had previous experience in psychodynamic therapy, they comment (favorably) on this difference from their previous therapy much more often than they comment on the structure of the sessions or the specific intervention techniques. Second, a number of empirical studies have compared client ratings of cognitive-behavioral therapists with client ratings of psychodynamic therapists. The studies I remember have found that cognitive-behavioral therapists are percieved as warmer and more empathic while psychodynamic therapists are experienced as cooler and more distant.
When I think back to my own experience as a client, I remember my therapist as spending most of the session sitting contentedly, nodding as I talked, saying little, and having his eyes closed much of the time. Therapy was helpful but I ended up with little idea of what he thought and no suggestions from him as to what I should do in real life. I can't imagine that Gary or any of my other clients experience me in that way.