Organisms are machines (broadly understood, anyway). Thus, since we as humans are thinking organisms, we are machines that think—we are organic thinking machines, as arguably are a variety of non-human animals. Some machines are artifacts rather than organisms, and some of them arguably think (broadly understood again). Such things are artifactual thinking machines—computers and the like are examples of this.
An important question is whether there is a deep ontological divide between organisms and artifacts generally. But rather than addressing this directly we'd like to ask a different albeit related question: are there deep differences between the kind of thinking organisms exhibit and the thinking artifacts like machines are capable of, between organic and artifactual thinking? This is not a question about the definition of English words like "think, "thinking", "thought", and so on. There's little depth to the question of whether, for instance, information input, processing, and output that computers are capable of is or ought to be captured by such terms. Rather, the issue is whether what things like us do and what things like computers are capable of doing—call those activities and capacities what you will—are categorically different.
Recent empirical findings in affective science, coupled with recent philosophical theorizing, suggest a deep divide indeed. Suppose you are on a hike and you encounter a mountain lion. What's going on with you at a psychological level? If you are like most of us, presumably you have, on the one hand, a rapid of stream of thoughts—"I'm going to die", "This is really bad luck", "I need to stay calm", "Wait, are there two of them?", "I should have read more on what to do in this kind of situation", and so on. On the other hand, you have a myriad of feelings—surprise, fear, and so on. So you have some cognitive goings-on and some affective goings-on.
Recent work in psychology and philosophy suggests that the cognitive and the affective are deeply unified. Not only may one influence another to a lesser or greater degree in a variety of contexts, but there is in fact a single cognitive-affective process underlying the appearance of two parallel and interacting process that can be teased apart. Lots of the kind of "thinking" we normally do is holistic in this way—the kind of information processing we normally engage in is cognitive-affective rather than purely cognitive. To the extent that we can extract a purely cognitive process we may engage in, it's merely derivative from the more basic unified process. (To understand the point here, it may not be far fetched to draw an analogy with entanglement qua non-separability.) This is not a system 1 vs. system 2 distinction, where the former is explicit and deliberate and the latter largely automatic and unconscious. The suggestion is rather that processes at the level of both system 1 and system 2 are themselves holistic, i.e. cognitive-affective.
There is no good evidence to believe (at this point, anyway) that artifactual thinking machines are capable of this kind of cognitive-affective information processing. There is good evidence that they may become better at what they do, but they simply don't process information via unified affective-cognitive processes that characterize us. The information processing they engage in merely resembles only part of the unified processing that's characteristic of us. This is not to say that things like computers can't feel and so that they can't think. Rather, that what the kind of thinking they do is categorically different from the one we do.
May in some not-so-distant future or not-too-distant possibility non-organisms engage in organic thinking? It's not clear. If there is indeed a deep divide between one and the other kind of processing, and if one is indeed characteristic of thinking organisms and the other of artifactual ones, then there is a deep divide between thinking organisms and thinking artifacts. So the relevant non-organisms would have to be very different.