lever at crank, connected by chain to lever at rear wheel
a pulley
gears and wheel and axle
That bicycle has 18 gears.
Bicycles with external gears have two, one guide pulley and one tension pulley, both in the rear derailleur. Some bicycles have further pulleys on the frame for either the brake or the shifter wire to run over.
Chains mesh with sprockets without slipping. A pulley system would need to use higher tension(and suffer higher losses) to avoid slipping.
an average bicycle has up to 24 gears but a bicycle has up to 30 gears
The bicycle is not a simple machine, there are too many interacting moving parts.
pulley
pulley
pulley
On a bicycle, as seen from the right(drive) side, the chainwheel(s) and the sprocket(s) and the chain will be rotating clockwise. If the bike has a rear derailer the tension pulley will also be rotating clockwise while the guide pulley will be rotating counter-clockwise. If the bike has an internally geared hub the gears inside there can rotate in different directions (or not at all) depending on what gear the bike is in.
The gears on the rear wheel are called a cassette
Because wheel and axle pulley and gear are simple machines