Consent is also a noun or a verb.
Agree is a verb only. Agreement is the noun form.
As a noun.
"Did you receive his consent before proceeding? ".
"Did you come to an agreement before proceeding?".
In this respect they mean the same.
As a verb.
Consent means to give permission to do something.
Agree also means this, BUT it has additional meanings which consent does not.
"I consent to you conducting a search of my premises" (Agree is interchangeable)
"You partner does not seem to agree with you" (consent cannot be used here)
"She'd eaten something that did not agree with her". (consent cannot be used here)
"I'm not sure that I agree with your view of America" (consent cannot be used here)