For certified aircraft, the FAA permits major modifications via many regulatory pathways, but the two most common in the GA fleet are via a Form 337 or a supplemental type certificate (STC). A Form 337, Major Repair and Alteration (Airframe, Powerplant, Propeller, or Appliance) is the documentation required for one-off repairs or modifications to an individual airframe, engine or prop. Supplemental Type Certificate (STC) modifications are more of a blanket approval designed to cover an entire family of aircraft types.
An STC is a more robust standard than a simple Form 337 that requires more engineering and proof that the intended modifications result in an airworthy plane. In many cases, an STC includes a supplement to the POH or flight manual that notates the changes and identifies how they affect aircraft performance.
Technically, both STCs and 337s meet legal requirements, but 337s can reflect different FSDO sensibilities with respect to documentation and testing. If you see 337s or STCs in an aircrafts documentation, they are a testament that the modifications meet the standards of both the mechanic performing the work and the FAA Flight Standards District Office (FSDO) inspector. An aircraft sporting modifications lacking a 337 or STC should be cause for investigation.
Experimental aircraft can fall into this category. Modifications or departures from kit designs or plans are relatively common. Often the novel change is approved through the flight test period, but other performance parameters may remain untested.