While Matthew 28, and Mark 16 are both referring to the great commission, and while they both sound similar, they are not exactly saying the same thing precisely.
Matthew 28:18-20 says:
“And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth. Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen.”
Mark 16:15-18 says:
“And he said unto them, Go ye into all the world, and preach the gospel to every creature. He that believeth and is baptized shall be saved; but he that believeth not shall be damned. And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues; They shall take up serpents; and if they drink any deadly thing, it shall not hurt them; they shall lay hands on the sick, and they shall recover.”
Matthew 28 - All power is given unto me in heaven and in earth.
Mark 16 - This saying is absent in Mark.
Matthew 28 - Go, and teach all nations.
Mark - Go into all the world and preach the gospel to every creature.
They are similar but not exactly the same.
Being told to go out unto all nations, and to go out into the world are the same.
However, to be told to teach all nations and to preach the gospel to every creature are two different things.
Teaching whatever Jesus commanded them vs. preaching the gospel is a different set of instructions.
Matthew 28 - Teach them to observe all things whatever I commanded you.
Mark 16 - This saying is absent in Mark.
Matthew 28 - I am with you always even unto the end of the world.
Mark 16 - This saying is absent in Mark.
Mark 16 - These signs shall follow them that believe, in my name they shall cast out devils, they shall speak with new tongues, they shall take up serpents, and if they drink any deadly thing, it shall not hurt them, and they shall lay hands on the sick, and they shall recover.
Matthew 28 - This saying is absent in Matthew.
The points on baptism are different in both Matthew and Mark.
Notice.
Matthew 28
Go ye therefore and teach all nations baptizing them in the name of the Father, and of the Son, and of the Holy Ghost.
Mark 16
Go ye all into the world and preach the gospel to every creature. He that believes and is baptized shall be saved, but he that believes not shall be damned.
The point on baptism is different and not the same.
In Matthew: The point on baptism is on baptizing in the name of the Father, Son, and Holy Ghost.
In Mark: The point on baptism is believing and being baptized to show one is saved, and if one believes not they are damned.
You may disagree, but seeing the points on baptism are different between Matthew, and Mark, I interpret them each differently in regards to their mention on baptism.
In Matthew 28, I believe that the teaching of all nations is to immerse (or wash) them in the name of the Father, Son, and Holy Ghost. The teaching part is what baptizes (i.e. immerses or washes) them in the name (or the authority of) the different persons of the Godhead or Trinity.
In Mark, I believe Jesus is saying that he that believes and is baptized into the Holy Spirit shall be saved. This makes sense because believing happens first and then one is gifted with the Spirit (Spirit baptism) afterwards. The person who does not believe automatically will not be Spirit baptized because of their unbelief. One needs to believe in order to have the gift of the Spirit.