There are two main ways to make and register an NFA item using a Form 1 - as an individual, and as a legal entity (corporation, trust, etc.). Historically trusts have been useful for a variety of reasons, but with the upcoming changes from ATF 41P, some of those reasons will be going away.
Here is how they work NOW:
Individual: You file a Form 1 using your own individual name. On the form you must provide photos, fingerprint cards, and get a signature from your chief of police.
Trust: You establish a trust either through a lawyer you hire or though one of the many services online that generate NFA trusts. Once the trust is established, you can use for any number of NFA items. You file a Form 1 using the trust name, and sign as a trustee of the trust. You do not need to provide photos, fingerprint cards, or get a signature from the chief of police.
Here is how things will work after July 13, 2016 (when the new ATF 41P rule goes into effect):
Both Individual and Trust Form 1s must provide photos and fingerprints. Trusts must provide them for all Responsible Persons on the trust. The requirement for chief of police signature has been eliminated, now you must only notify them.
So as you can see, going the trust route was useful to save the effort of getting photos and fingerprints done, as well as getting signatures from the chief of police. Soon there will be no need for signatures, and you will have to provide photos and fingerprints regardless of whether you file individually or as a trust.
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Form 4 if you have an existing SBR transferred to you. Form 1 if you are making an SBR yourself.