Is there any way to differentiate between a redshift caused by recessional motion vs. gravity? How certain, if at all, are astronomers that the redshift they are measuring is relating to recessional motion as opposed to gravity?
 A: I don't think that would even be considered. If you consider Hubble's law - once we get out of our neighbourhood and into the Hubble flow, then what we see is that identically in every direction, the redshift is proportional to the distance we measure to objects by independent means.
An explanation involving roughly stationary objects that emit light with a gravitational redshift would require a bizarre correlation between mass and distance and requires this to be the same in all directions, such that our Galaxy is at the centre of a symmetric distribution.
Plus if you do the Maths - giving galaxies a substantial redshift requires missing mass that puts dark matter to shame - there is no evidence for such extreme masses from galaxy rotation curves or the dynamics of clusters. i.e.
If we say a the light from a resolved galaxy at $z \sim 0.1$ (comparatively modest) comes from a region that is basically 10 kpc in radius, then a rough estimate can be obtained from
$$ z \simeq \frac{GM}{Rc^2}$$
$$ M \simeq z \frac{Rc^2}{G}$$
Thus the required mass to produce a gravitational redshift of $z=0.1$ would be more than $10^{18}$ solar masses!
However, to answer the headline question - if all you have is a redshift and no other information ( or theoretical or philosophical objections) then there isn't a difference between a cosmological redshift and GR redshift.
