Unitary- one central government controls everything. Ex. U.K. France, Spain
Confederate- a voluntary or weak association of independent states that agrees to follow a powerful central government. Ex. Cofederate states of america, Russian federation

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Ok, you got me. I read it wrong. Yes, your understanding of Unitary is correct. However, a confederation is generally not following a strong central government but a weaker one so they don't lose their independent status. There is a slight difference between a Federal government like the US and the USSR and a looser confederation like the CSA and the current Russian Federation.