If baptism is an "an outward and visible sign of an inward and spiritual grace" (BCP), then we can ask three questions, from which I think you can identify different theologies of baptism.
Who makes the sign?
- God through the baptiser;
- The baptiser; or
- The baptised.
Is the grace
- already present;
- given by the act; or
- anticipated in the act?
What is the grace signified?
- A new status;
- A new nature; or
- Both.
I think most credo-baptists believe that the baptised makes the sign of an already present new status and new nature. The Reformed essentially believe that God through the baptiser makes the sign of an already present new status (although the sign is also of the new nature that may be either already present, given by the act, or anticipated in the act). The RC and the Lutherans seem to believe that God through the baptiser makes the sign of a new status and new nature which are given by the act.
I think I would say that God through the baptiser makes the sign (because the baptised is always described as passive in the NT), the grace is given in the act (because the NT seems to see baptism as achieving something), the grace signified is the new status (because that seems to fit the NT texts when interpreted in the light of wider theological convictions and experience - namely the once for all nature of the new birth and the reality that many baptised people do not believe). However I'd also say, with the Reformed, that the new nature may be either already present, given by the act, or anticipated in the act.
How would you answer the three questions?
NB I wouldn't usually chose to use the word grace in the way it is used in this standard definition. It makes grace sound like a 'thing'. Maybe we could use the word 'reality'.