Is Tarot like a Ouija board? I would say that, in my experience, the short answer is "no."
The longer answer is tied up with the question of, "what exactly is divination?" Which in turn is intimately linked with the question of "what is the nature of reality? How does the universe 'work?'"
~~~~
There is a certain streak of thinking in some Fundamentalist Christian viewpoints that anything seemingly paranormal or supernatural must be caused by some sort of uncanny "power," which can only come from one of two sources: God or Satan. Such power is called "spirit" by some, and thought to be transmitted by disembodied entities, or "spirits." Spirits can only be from Heaven or from Hell. Therefore, goes the logic, anything that seems miraculous must be either holy or diabolic, with no middle ground between.
Of course, "paranormal" and "supernatural" (literally "beyond the normal" or "above the natural") seem, in practice, to mean anything that appears to be beyond what we humans currently understand well.
Divination, or fortune-telling, doesn't seem possible by the current state of human knowledge; therefore, divination must be caused by supernatural means (that is, by spirits). Using Tarot, by this theory, is a method of getting information that must be coming from spirits; the Ouija board is a method of summoning spirits. Therefore, fortune-telling and spirit-summoning must be practically the same thing.
So, IF that's your only model of reality, then yes, you'd have no choice except to assume that Tarot and Ouija are very much like each other.
~~~~
...but in my own personal experience, Tarot doesn't seem to involve spirits at all. I've had a little experience with spirits...very little, true, but (I think) enough to recognize a certain "feel" to the energy of a room when they're around and actively taking parts in things, at least some of the time. I've never gotten that feeling with Tarot.
As for how Tarot works, if not by spirits, well, there are several competing hypotheses...
One is that we humans, being possessed of a soul, are in fact part spirit; and that whatever knowledge spirits can access, we can theoretically access as well, due to our very nature. Of course, most of the time we're so distracted by physical reality that we can't really distinguish those bits of knowledge; and that Tarot and other divination methods are a way of "distracting" the parts of our mind that are stuck in the material level, so that some of those other bits of knowledge can squeeze through.
Another theory is that Tarot is a way of trying to pick up patterns from the fabric of reality. You know how fractal equations form the same patterns in small scale that they do in large scale? Well, one model of the universe theorizes that patterns of events behave in a similar way: that large-scale events might be mirrored in small-scale ones. Randomized results might reflect those patterns, so by studying the one, you can gain some glimpse of the other.
Another theory is that Tarot works by natural laws that we just don't understand yet. People in former times didn't understand the forces of weather, or disease, or earthquakes, or other perfectly natural phenomena; therefore, they ascribed them to spirits: gods and devas and daemons and faerie-folk and whatnot. But now we can observe things beyond our own human senses, and consequently we know a bit about the behavior of the atmosphere, the lives of bacteria, and the effects of plate tectonics; what was once "paranormal" or "supernatural" are now seen as entirely normal and natural. Therefore, it's likely that Tarot and other seemingly uncanny things will, one day, be understood...we simply haven't developed the measuring devices yet to detect their causes.
And then, of course, there's the "agnostic" viewpoint, which goes, "I have no idea how it works, and until human knowledge catches up, I'm not going to speculate. But since it does seem to work, I'll use it and see what information I can get from it."
I tend to vacillate among all of those...and I'm sure there are many, many more hypotheses that I'm not familiar enough with to mention here. The point I'm trying to make is that just because we don't know what causes something doesn't mean that it has to be spirit of some sort (OR that spirits can only be holy or unholy, for that matter).
Tarot and Ouija can only really be considered the same thing if you accept a certain narrow view of reality as absolutely true; otherwise, they seem to behave by different rules, and have different results. If you lump everything "not known" together and assume it's all related, then of course they both fall into that category; but I believe the history of knowledge and how we gain it argues against such an idea. The only safe assumption about the unknown is not to assume anything about it at all, but to wait and see what we may learn about it in the fullness of time.