T213-2's basically were trying to use images they already had in stock (from T206's) and tried to update them to some degree to make them more current (usually only the caption though as they tended not to care if there was a team insignia/name/etc. on the front that may clash with the team identified on the bottom.) In some cases they got mixed up--the classic example is the "Chappelle" card in the set.
Initially they (correctly) made a card using Bill Chappelle's T206 image to depict him for the 1914 Brooklyn Fed's but then they reissued the image of "Bill" but this time with Cleveland--which was a mistake as that was Laverne "Larry" Chappell that played w/ Cleve in 1916. So, their intention may have been to issue a card of the Cleveland Chappelle/Chappell and mistakenly thought they were the same guy--but they weren't.
Interesting tid-bit on Larry Chappell is that he died in S.F. after having played w/ the Salt Lake team of the PCL in 1918 during the Spanish Flu pandemic that plagued the country that year. Here is (I believe) the only card of Chappell ever produced that actually used his own image...
-Rhett