What is the difference I hear you ask?

For most people the answer would be ‘nothing’.
Whether you sit on a shoulder press machine and press your equivalent body weight above your head or kick up into a handstand (against a wall ) and lower head to the floor and push back up again, there does not seem to be a difference.
You would think that if you could do one, then you could do the other.
Well in 99% of cases, that is not the case. Surprisingly, for most people and especially those who lift weights, handstand push ups are far harder to perform than shoulder presses.

In a shoulder press movement, and especially on a seated press machine, you do not use a single muscle to balance yourself. By using the secondary muscles in the shoulders, you are working them a lot more and from different directions as you keep balance in a handstand push up. More effort is needed and greater shoulder strength required to perform a handstand push up.

Other benefits of handstand push ups are in increase in blood flow to your brain and vast improvements in spatial awareness. Most people, who have never tried to do a handstand, or rarely find themselves upside down for that matter, become disorientated and lose their bearings.
After only a few attempts, your brain becomes used to seeing things from a different perspective, which greatly improves spatial awareness, and with the increased blood flow, improves your well-being.

Handstand push ups also offer much more range of movement. When performing shoulder presses, the weight bar is lowered as far as the tops of the shoulders, and then pressed back up.
When you become stronger and more confident at performing handstand push ups, you can raise your hands by placing them onto books and even chairs. A handstand push up between two chairs almost doubles the distance you have to travel until your head touches the floor and is an extremely impressive feat of strength.

On top of all the health and strength benefits of handstand push ups, you do not need to visit a gym or spend money on weights for a home gym.
Handstand push ups can be performed at home and build tremendous shoulder and upper body strength that far outweigh the benefits of using weights.

If you find, you do not have the strength to perform a single push up, start by kicking into a handstand (against a wall) and just hold this position for time. The strength gains from just doing this will be dramatic.
If you want superior upper body strength that will blow you away, then turn your training upside down and include handstands into your daily routine.