Hi Nathan,
There are several options.
Grayscale (Intensity)
The value is expressed as absolute hight from the original point position and only in positive values. A second version (centered) uses mid gray value for the original point position and has the option to move the point “up” and “down”.
RGB
The values express an X,Y,Z position and allows so to overcome limitations of the gray values, as they are only “up” and eventually “Down” values for a specific point.
In this way, points can move relatively free and even on top of each other. The downside is, the are not really editable anymore in an image app, gray values are more “human-readable”.
The RGB or XYZ values are differentiated in RGB (XYZ Object), RGB (XYZ World) and RGB (XYZ Tangent)
There are subsets of color based Displacement maps available, kind of Double Gray versions in Red and Green, for up or down values. Mostly, from my point of view, to overcome the 8bit/channel limitations.
I highly recommend for critical work 16bit/channel (at least) and never color profile these channels, they are data channels and do not need a gamma or a log curves applied to them. 32bit/channel/float and linear is certainly the best way to do it now. OpenEXR as format is the industry standard.
Your question: if you really want to use grayscale (Intensity), your result will be eventually different, in some cases heavily, from the sculpting result you had. Yes, you can go to “Settings” in the Sculpt-Bake-Menu and set what you like to have.
All the best