They were geographically close by; I see addresses for Dynacomp in Rochester and Webster, and for Artworx in Penfield and Fairport, all in New York State. However they were separate companies, as recounted by Art Walsh in ANTIC interview #284. He founded Dynacomp with Fred Ruckdeschel in 1978, but they ended up splitting the company up. Fred bought Art’s share of Dynacomp, and they split the software catalog in two. Art took two of the local programmers who were working for Xerox in Rochester at the time, and created Artworx, officially incorporating in 1981.
This is supported by other sources. In particular, this Dynacomp catalog mentions its “Bridge 5.2” product, which won a bridge tournament, competing against “Troup’s Bridge Baron and Artworx’ Bridge 4.0”. Additionally, the same catalog mentions that Dynacomp’s founder and president was Dr. F. R. Ruckdeschel, whereas this Artworx catalog and its defunct web site mention that Artworx’ president was Arthur M. Walsh.
Some titles, such as Rings of the Empire, do appear in both companies’ catalogs, but there are many titles which are unique to Artworx and Dynacomp (although these lists of Atari games may not be exhaustive).
One of Artworx’ major titles, Bridge, developed by Art, was released in multiple versions, the earlier ones published by Dynacomp, before Artworx was founded. When Art founded Artworx, he took Bridge with him; but it seems Dynacomp continued publishing later versions, only on the Commodore 64, so perhaps Artworx and Dynacomp both continued developing it separately. Artworx’ other major title, Strip Poker, doesn’t appear in Dynacomp’s catalogs; it was published after the split, after Jerry White (ANTIC interview #124) brought a poker program to Artworx.