In legal speak the term 'build' and 'assemble' fall into two different catagories.
The term 'build' will usually apply to the construction of a firearm from scratch using base materials,
Am individual may 'build' a firearm for personal use.
The receiver of the constructed firearm must contain a serial number individual and unique to that firearm.
An individual may not 'build' firearms and introduce them into the retail trade without a License to do so obtainable from the BATFE.
The term 'assemble' is used to identify a firearm constructed from parts already machined and intended for construction into an individual firearm.
Assembled firearms use component receivers already built and serial numbered by a company licensed to manufacture firearms along with component pieces manufactured 'for the trade'.
One must follow all laws pertinant to taking possession of the numbered receiver intended for the trade, in other words all laws and regualtions pertaining to obtaining, recording, and lawfully selling, obtaining the serial numbered receiver component are followed.
A Gunsmith assembling a Mauser rifle from a pre-existing receiver is an example of this.
The firearm can be subsequently sold again by the end user as long as all state and federal laws are followed.
A gunsmith, or individual, manufacturing a firearm from a customer, or individual, supplied set of blueprints using base material would constitute 'building'.
This particular firearm would have to be serial numbered and logged as such.
An individual is allowed to 'build' a firearm using base materials but would not be legally allowed to sell the firearm to a second party, the firearm would be strictly for that individual's use.
A gunsmith may 'build' a firearm from base materials for the use of a individual but the gunsmith, being employed 'in the business', would have to possess a license for manufacturing firearms for the trade.
The firearm 'built' by the gunsmith employed in the business may be susequently resold by the individual taking possesion, as long as all pertinet laws regarding the sale of firearms in that individuals locale are followed.
No full automatic firearms may be manufactured or 'built' with the exception of firearms manufactured or assembled for the use of Military or Police forces legally allowed to posess such material.
Full automatic firearms may be assembled using pre-existing serial numbered receivers already on the civilian market that have been assembled into a functioning full automatic firearm prior to the enacting of the machine gun ban.
Short barrel firearms fall into another catagory and short barrel full automatic firearms may, or may not, be allowed and legal be they' built' or 'assembled' depending on the individual state laws and regulations.
I have tried to make this as easy as possible to follow and comprehend but the legal speak in the actual books of regulation still jar me.HTH