According the Robert Wright in The Continental Army, page 238, Webb's Additional Continental Regiment was authorized on 11 January 1777. It was organized in the spring of 1777 to consist of eight companies.
The regiment was assigned to the Highlands Department from 14 April 1777 to 22 July 1778 and was then assigned to the Eastern Department until 17 November 1779 when the regiment was assigned to the Main Army.
On 9 April 1780 the regiment was reorganized to consist of nine companies. The regiment was then 'adopted' by Connectifut and was redesignated as the 9th Connecticut Regiment. In October 1780 Stark's Brigade, to which the now 9th Connecticut was assigned was reassigned to the Highlands Department on 7 October 1780.
On 1 January 1781 the 9th Connecticut was consolidated with the 2d Connecticut Regiment.
The following information is from the same volume, pages 233-234:
The 2d Connecticut Regiment was authorized on 16 September 1776 and was organized between 1 January and April 1776 and consisted of eight companies. The regiment was assigned to the Highlands Department on 3 April 1777.
The regiment, in various brigades, was assigned to the Highlands Department until 13 November when the regiment was assigned to the Main Army until 1 May 1779 when it was reassigned to the Highlands Department.
On 11 July 1779 the regiment was reorganized to consist of nine companies.
The 2d Connecticut was consolidated with the 9th Connecticut Regiment on 1 January 1781 and the unit was redesignated the 3d Connecticut and consisted of nine companies. The new unit was furloughed on 15 June 1783 at West Point and was disbanded on 15 November 1783.
Webb's regiment and the 2d Connecticut were not the same regiment until they were consolidated in January 1781 into a redesignated regiment, the 3d Connecticut.
A Colonel Webb did command the 2d Connecticut, but it was Colonel Charles Webb who commanded it from 1 January 1777 until 13 March 1778.
Colonel Samuel Webb was the commander of Webb's Additional Continental Regiment that became the 9th Connecticut Regiment and then was finally consolidated with the 2d Connecticut Regiment to become the 3d Connecticut Regiment.
From The Encyclopedia of Continental Army Units by FA Berg:
'3d Connecticut Regiment of 1781: Created on January 1, 1781a by a merger of the former 2d and 9th Connecticut Regiments. The regiment served until around June 3, 1783 when its veterans were furloughed and its recruits were pooled into the sole surviving Connecticut Regiment.'-19
The regimental commander was Colonel Samuel Webb from 1 January 1781 to June 1783.-19
The 9th Connecticut is listed as having been previously designated Webb's Additional Continental Regiment and was redesignated the 9th Connecticut on 18 July 1780 (page 22).
Berg lists 3 regiments designated the 2d Connecticut, those of 1775, 1777, and 1781.-18-19.
Berg lists three regiments designated as the 3d Connecticut of 1775, 1777, and 1781.-19.
Berg lists only one regiment designated as the 9th Connecticut which was commanded by Colonel Webb-22.
The entry for Webb's Additional Continental Regiment on page 136:
'Webb's Regiment was created on January 1, 1777. It was raised mostly in Connecticut and was perhaps the most successful of all the additional regiments. Somehow Webb's Regiment was always in uniform-they wore scarlet coats and the regiment seems to have been well-trained and effective in battle. It even had a band. In mid-May 1780, Connecticut moved to take the regiment into its quota and this was approved by Congress on June 23. The regiment was numbered the 9th Connecticut on July 18, 1780.'
In Military Uniforms in America, Volume I, edited by John Elting on page 76-77 Webb's Regiment is discussed and the scarlet uniforms shown. It states in the second to the last paragraph that 'In July 1780 it was redesignated the 9th Connecticut Regiment.'