The difference between Approve and Consent

When used as verbs, approve means to sanction officially, whereas consent means to express willingness, to give permission.

Consent is also noun with the meaning: voluntary agreement or permission.

check bellow for the other definitions of Approve and Consent

Approve as a verb (transitive):

To sanction officially; to ratify; to confirm.

Examples:

"Although we may disagree with it, we must nevertheless approve the sentence handed down by the court-martial."
Approve as a verb (transitive):

To regard as good; to commend; to be pleased with; to think well of.

Examples:

"We approve the measure of the administration, for it is an excellent decision."
Approve as a verb (transitive, archaic):

To make proof of; to demonstrate; to prove or show practically.
Approve as a verb (intransitive):

To consider or show to be worthy of approbation or acceptance.

Examples:

"Note: This word, when it signifies to be pleased with, to think favorably (''of''), is often followed by ''of''."

Approve as a verb (transitive, legal, English law):

To make profit of; to convert to one's own profit — said especially of waste or common land appropriated by the lord of the manor.

Consent as a verb:

To express willingness, to give permission.

Examples:

"After reflecting a little bit, I've consented."
Consent as a verb (medicine):

To cause to sign a consent form.
Consent as a verb (obsolete):

To grant; to allow; to assent to.
Consent as a verb:

To agree in opinion or sentiment; to be of the same mind; to accord; to concur.

Consent as a noun:

Voluntary agreement or permission.
Consent as a noun (obsolete):

Unity or agreement of opinion, sentiment, or inclination.
Consent as a noun (obsolete):

Advice; counsel.