The surveyor was a government employee, and it was his responsibility to fix the boundaries of the tract as accurately as possible. As may be expected, having the land surveyed cost money. In Tennessee at least, having the land surveyed was the point at which the claimholder also became liable for property tax. In some states, a warrant was locally issued at this point to instruct the State to issue a grant. Finally, the grant was made by the government and a deed issued.
Patent is another term that is used for grant.
In some cases patent is used to imply a grant made by a Colony, with the term grant being reserved for use by States. Note that not all steps were uniformly used in all Colonies. Thirty of the states were settled as Public Domain States where the Federal Government acted through a Land Office as the means of granting land. A similar process of claim, survey, etc. was used, with an additional residence requirement in place prior to grant issuance. Tennessee was unusual in that it was part metes and bounds and part Public Lands.