When I want to go to the root, I write the following:

su - root and press enter
Then I get the following message.
password:

I write my password : nicosiar and press enter

This way I am in the root.

[root@h27n2fls301o1037 root]#
--------------------------------------------------------------------------

I can do the same thing in different way.

First I write su and press enter
Then I get the following message
password:

I write the password: nicosiar and press enter
Now I am in a different root.

[root@h27n2fls301o1037 heden]#

My question is what is the difference between the two different roots?

I have seen that just writing su would be enough to go to the root when installing software.
What are those differences?

You aren't in a different root, but your environment (the variables and their values) are different.

With just "su", you keep your present environment. With "su -", it's as though you logged in as root - any environment variables you had are (temporarily) tossed, and you pick up the same ones root has if it logged -n - you actually run the same files (.bash_profile etc.)

By the way, if you are root, you can "su - someotheruser" to login as that user without knowing their password.

--
Tony Lawrence
http://aplawrence.com