A motion sensor simply detects motion. Person A, person B, the dog, the air conditioner coming on: it's all the same to a motion sensor. It also can't tell the difference between a person coming in or going out.
The term "occupancy sensor" or "occupancy switch" is used by some lighting companies who make devices for office buildings and hotels to mean a light switch with a built in motion sensor.
However, the term "occupancy sensor" is also used for an entirely different kind of device: one that either counts how many people are in a room, or one that tracks specific individuals.
Secure facilities, including some hospitals, track individual people, usually by a badge or wristband. Think Star Trek: "Computer, where is Ensign Silver?" "Ensign Silver is in Holodeck 4." That's occupancy.
But there's no fixed definition for an "occupancy sensor." There are a bunch of different possible technologies. Most are too expensive, or too complex, for cheap DIY home automation right now, although everyone expects this to be common in a few years.
Quite a few home automation companies now use the term "presence sensor" instead, as SmartThings done. Probably to distinguish it from those office building switches. "Michael is home," not just "something moved."
Another term is "microlocation," used to distinguish further between a presence sensor that covers a large area, typically a whole house, and "Michael is in the living room."
Quite a few people believe future microlocation will be based on a device that can listen for heartbeats, recognizing some individuals but also being able to respond to strangers. Which is both cool and creepy.
So a "motion sensor" detects motion. An "occupany sensor" could be any of many technologies used in different ways, the term has a lot of different meanings.
Did that help? In a home automation discussion, people often use "occupancy" to mean microlocation: "Michael is in the living room; Charlie is in the kitchen." But while systems to do this exist, they're very expensive and don't interface directly with SmartThings. So a lot of people try to build their own cheaper versions.