Is the amount of tax that consumers pay the same as the amount producers pay? I am confused about the amount of tax producers and consumers pay.

On this diagram, I can see that the supply curve increases by twenty dollars, as the tax is 20 dollars. The consumers have to pay 10 dollars more from what they previously had to pay.

This confuses me a bit. Don't producers and consumers pay the same amount of tax? When I look at this, it seems like they pay a different amount. The consumers pay 10 dollars more, but the producers don't pay $10 more.
Tax is payed by the party it’s levied on, but I think your question is about tax burden and loss of consumer/producer surplus. 

In this case both producers and consumers loose the same amount of their surplus, as you can calculate the lost area which is for both of them 40.

However, in real life this does not have to be symmetric. It depends on the elasticity of the demand and supply. As a general rule the more elastic demand the higher share of the tax burden goes on producers and the more elastic supply the higher share of burden is shifted to consumers.