Motors are generally segmented by how they are actuated. A brushed motor is physically different from a stepper and thus is actuated differently. The difference, however, is actually how the actuation is initiated & controlled. But there is far more that differentiates motors and the differences matter when choosing the appropriate motor for an application:

• Physical dimensions of body & shaft
• Weight
• Mounting options
• Shaft shape
• Shaft options like double ended, extended & threaded
• Output attachments like gears, pulleys & vibrating weights
• Cost
• Availability, sourceability
• Operating Voltage (max, starting)
• Speed (no load/loaded), Current (no load/loaded/stall), Torque (starting/stalled)
  • Sometimes datasheets will include a load to give you a better real-world estimate
• Operating temp
• Output modifier like gears and the gearing scheme (spur, planetary)
• Non-standard output layouts, like right-angle. These are my favorite and I've never had a use for them.
• Sensing option for closed-loop systems (encoders, pots)
• Built-in controllers if you wanna get all fancy
• Motor type-specific attributes like number of coils or magnet type
• Robustness (better term?) like bearing type, gearing material & type of encoder

That's a lot of differences to consider! Am I missing any?