I became sufficiently interested in these discrepancies to do a little research. I knew many of the names that ADB uses come from the Star Trek Technical Manual by Franz Joseph (which is where ADB originally got its licence from in 1979-the licence with Paramount came later, after SFB became popular)but I was increasingly curious. Frankly, I'd never bothered comparing them before because the canonical NCC list is about as messed up as the one ADB uses.
From Memory Alpha:
Constitution Class Starships:
USS Constellation (NCC-1017)-This one is there in ADB's list and is correct.
USS Intrepid (NCC-1631)-Discrepancy-ADB=NCC-1708 (NCC-1708 is consistent with the Star Fleet Technical Manual (published 1975); The NCC-1631 comes from the Star Trek Encyclopedia, 1994, which is not strictly canonical, and was used in REMASTERED ST:TOS, 2008)
USS Potemkin (NCC-1657)-Discrepancy-ADB=NCC-1711 (NCC-1711 is consistent with the Star Fleet Technical Manual, 1975; NCC-1657 was established in ST:VI The Undiscovered Country, 1991)
USS Excalibur (NCC-1664)-Discrepancy-ADB=NCC-1705 (NCC-1705 is consistent with Star Fleet Technical Manual, 1975; NCC-1664 originates from Greg Jein's article, The Case of Jonathan Doe Starship, 1973, and was used in Star Trek Encyclopedia, 1994, and again in REMASTERED ST:TOS, 2008)
USS Exeter (NCC-1672)-Discrepancy-ADB=NCC-1706 (NCC-1706 is consistent with Star Fleet Technical Manual, 1975; NCC-1672 was first used in REMASTERED ST:TOS, 2007)
NCC-1700 (Presumed to be USS Constitution)
USS Enterprise (NCC-1701)-Right
USS Enterprise (NCC-1701-A)-Right
USS Hood (NCC-1703)-Discrepancy-ADB=NCC-1707 (NCC-1707 is consistent with the Star Fleet Technical Manual; The NCC-1703 comes from the REMASTERED ST:TOS, 2008)
NCC-1707 (Was supposed to be a refit constitution named Intrepid, but was not shown on film, ST IV: The Voyage Home, 1986)
USS Lexington (NCC-1709)-Discrepancy-ADB=NCC-1703 (NCC-1703 is consistent with Star Fleet Technical Manual, 1975; NCC-1709 originates from Greg Jein's article, The Case of Jonathan Doe Starship, 1973, and was used in Star Trek Encyclopedia, 1994, and again in REMASTERED ST:TOS, 2008)
USS Defiant (NCC-1764)-Discrepancy-ADB=NCC-1615 (NCC-1615 is not consistent with Star Fleet Technical Manual, 1975, which does not list the ship at all; NCC-1764 originates from Greg Jein's article in T-Negative magazine, 1973, and was used in Star Trek Encyclopedia, 1994, in "In a Mirror, Darkly" 2005, and again in REMASTERED ST:TOS, 2008)
There are more Constitution-class registries, besides (those above are the ones shown conclusively on screen), but many of those come from Greg Jein or Michael Okuda and many of those were taken from the Star Fleet Technical Manual, anyway.
It is interesting that the Defiant, which was not listed in the Technical Manual, does not have an ADB registry of NCC-1764, corresponding to the show. However, it turns out that in the Technical Manual NCC-1764 is used for the USS Galina and ADB had already listed NCC-1764 as the USS Atlantis for SFB: Module R5 in 1992.
From Memory Alpha:
Constitution Class Starships:
USS Constellation (NCC-1017)-This one is there in ADB's list and is correct.
USS Intrepid (NCC-1631)-Discrepancy-ADB=NCC-1708 (NCC-1708 is consistent with the Star Fleet Technical Manual (published 1975); The NCC-1631 comes from the Star Trek Encyclopedia, 1994, which is not strictly canonical, and was used in REMASTERED ST:TOS, 2008)
USS Potemkin (NCC-1657)-Discrepancy-ADB=NCC-1711 (NCC-1711 is consistent with the Star Fleet Technical Manual, 1975; NCC-1657 was established in ST:VI The Undiscovered Country, 1991)
USS Excalibur (NCC-1664)-Discrepancy-ADB=NCC-1705 (NCC-1705 is consistent with Star Fleet Technical Manual, 1975; NCC-1664 originates from Greg Jein's article, The Case of Jonathan Doe Starship, 1973, and was used in Star Trek Encyclopedia, 1994, and again in REMASTERED ST:TOS, 2008)
USS Exeter (NCC-1672)-Discrepancy-ADB=NCC-1706 (NCC-1706 is consistent with Star Fleet Technical Manual, 1975; NCC-1672 was first used in REMASTERED ST:TOS, 2007)
NCC-1700 (Presumed to be USS Constitution)
USS Enterprise (NCC-1701)-Right
USS Enterprise (NCC-1701-A)-Right
USS Hood (NCC-1703)-Discrepancy-ADB=NCC-1707 (NCC-1707 is consistent with the Star Fleet Technical Manual; The NCC-1703 comes from the REMASTERED ST:TOS, 2008)
NCC-1707 (Was supposed to be a refit constitution named Intrepid, but was not shown on film, ST IV: The Voyage Home, 1986)
USS Lexington (NCC-1709)-Discrepancy-ADB=NCC-1703 (NCC-1703 is consistent with Star Fleet Technical Manual, 1975; NCC-1709 originates from Greg Jein's article, The Case of Jonathan Doe Starship, 1973, and was used in Star Trek Encyclopedia, 1994, and again in REMASTERED ST:TOS, 2008)
USS Defiant (NCC-1764)-Discrepancy-ADB=NCC-1615 (NCC-1615 is not consistent with Star Fleet Technical Manual, 1975, which does not list the ship at all; NCC-1764 originates from Greg Jein's article in T-Negative magazine, 1973, and was used in Star Trek Encyclopedia, 1994, in "In a Mirror, Darkly" 2005, and again in REMASTERED ST:TOS, 2008)
There are more Constitution-class registries, besides (those above are the ones shown conclusively on screen), but many of those come from Greg Jein or Michael Okuda and many of those were taken from the Star Fleet Technical Manual, anyway.
It is interesting that the Defiant, which was not listed in the Technical Manual, does not have an ADB registry of NCC-1764, corresponding to the show. However, it turns out that in the Technical Manual NCC-1764 is used for the USS Galina and ADB had already listed NCC-1764 as the USS Atlantis for SFB: Module R5 in 1992.