Key word "most often".
The DB601A1 was used for both types like the Bf110C and the Bf109E/F and I already mentioned the DB605A1 above.
Of course there were variants of the DB6xx for various applications that could easily generate a 2,000 word dissertation - but the short of it, is that the engines in the Bf110 were most often the same as in the Bf109.