The junction of the two dissimilar metals that interfaces with the target medium, the sensing junction, is enclosed in a sheath called a probe. A grounded thermocouple is one where the sensing junction is wired directly to the probe wall. The result is very good heat transfer from the target and a quick response time.
The sensing junction of an ungrounded thermocouple is electrically isolated from the probe wall. This results in a slower response time, but the electrical isolation of ungrounded thermocouples gives them some important advantages over grounded versions: They last longer, they interface more easily with instrumentation and they eliminate ground loop problems. (Ground loop problems stem from the unintended connection of a circuit to ground.
An exposed thermocouple is one where the junction is outside the probe wall and exposed to the target medium. They have the best heat transfer and quickest response time but are limited by the kinds of target media where they can be used. They would not be suitable for caustic or corrosive target media, for instance. In cases where quick response time is essential, the exposed thermocouple might well be the best choice.