What are the main differences between the penny farthing the safety bicycle and the modern bicycle?

The penny farthing had no gearing between the pedals and the front/drive wheel, so the front/drive wheel had to be made really big to get any speed out of the bike. Then the rider had to sit nearly straight above the wheel axle to be able to steer and pedal. This made the bike prone to toppling forward while braking.

The safety bike had a chain between the pedals and the rear/drive wheel. By having a bigger sprocket by the pedals and a smaller at the rear wheel you could get the bike up to speed while still retaining a more practical wheel size and placing the rider between the wheels rather than on top. This meant you cold break with much less risk of toppling forward, hence the name "safety bike".

The modern "utility" bike is in principal very similar to the safety bike. It is most likely lighter, has better brakes and the ability to freewheel; it might have any number of gears, but the basics still remain.

Today we have all manners of specialized bikes, full suspension MTBs, flimsy road bikes and everything in-between.