The above Carter Coat-of-Arms belonged to Fred Broad, of Virginia, a now deceased descendant of the Carters of "Oakland," Virginia, who descended from CPT Thomas Carter III. Thus, these arms are the most likely Coat-of-Arms for CPT Thomas Carter, as they are the most authentic known for the CPT Thomas Carter family.
In English tradition Coats-of-Arms were awarded to nobility by the crown, thus MANY Coats-of-Arms exist for the Carter family.
Robert "King Carter," who displayed arms similar to the Carters of Garston and London were described as: "Argent a chevron sable between two roundels in chief and in base a Catherine wheel vert; the crest on a mound vert a greyhound sejant argent sustaining with the dexter paw a shield of the last charged with a catherine wheel of the first."
Interestingly, the "King" inscribed the words "Secretariat" at the bottom of the arms (note the above inscribed 'Fortudine' on these arms) which indicates Robert probably manufactured his arms to some degree.
The Carters of Bedfordshire, from which CPT Thomas Carter likley descended, had arms that were described as "Azure a talbot passant between three round buckles or. the crest: Out of a mural crown or. and azure a demi-talbot proper."
Regardless, CPT Thomas Carter's arms and Robert "King" Carter's arms are very similar, the most notable the talbot (or greyhound), and wheels, common to both.
For a scholary discussion of the early Carters, see Paul Carter's "New Origins" book, listed on this site.