A freewheel is an older technology that combines the freewheeling mechanism and the gears into one unit. It threads onto the hub of the rear wheel and contains both the ratcheting mechanism (which allows the wheel to spin freely when not pedaling) and the gears. In a freewheel, the gear cogs are a part of the freewheel assembly.
A cassette, on the other hand, separates the ratcheting mechanism (known as the freehub) from the gears. The freehub is a part of the hub, and the gears (cogs) slide onto the splined body of the freehub. This design allows for easier removal and replacement of individual gears (cogs) without having to replace the entire unit.
When upgrading or maintaining a bicycle's drivetrain, it's crucial to ensure compatibility between the freewheel or cassette, hub, derailleur, and shifter. Consulting with a bike mechanic or referring to the manufacturer's specifications can help in choosing the right component for your bike.