First, SHOULD you mention the step father in the invitations? Does the groom consider his step father to be a "dad"? Or is this based on the step father contributing financially? Parents' names are included in the invitations to make it clear who the bride and groom are, not to give glory to those who helped pay for the wedding. Are people being invited who think of the groom as "David Newman's (step) son" or is David Newman simply the husband of the groom's mother?
The honour of the presence of
[two blank lines to write in names]
is requested ... blah blah blah
Bonnie Bridette, daughter of
James Singleton and
Beatrice Bridette, to
Gordon Alexander Groomly, son of
Helen Groomly Newman and David Newman,
Gregory Newman,
on Saturday blah blah blah
Helen and Gregory divorced when Gordon was a child, and Helen subsequently married David who was has been a second father to Gordon. Gordon calls David's family Gramma, Uncle, and so on.
James and Beatrice are not married, but have been together for 25 years. Since they are together as a couple, their names can be on two seperate lines or together on one line.
You don't need to make your invitation as detailed as a family tree. If people don't know the groom's family well enough to understand this detail, that is OK. The idea is to give people a clue as to who Gordon is, as in "Do we know a Bonnie and Gordon? Oh I see, it's David's step son." If the people have no idea who David is, consider that a lot of people getting the information may not know who James or Beatrice or Gregory are. No big deal. You don't designate as parent or step parent, you recognize parents generically without distinguishing between bio daddys and step daddies.