The amount that an object in Draw is moved, is a factor of the scale of the drawing e.g., Tools > Options… > LibreOffice Draw > General > Scale section. By default this is 1:1 and at this scale these are the different movement amounts:
- Cursor key, unmodified: 1.0mm / ~0.04in / ~2.8pt
- Cursor key + SHIFT: 10.0mm / ~0.4in / ~28.3pt
- Cursor key + ALT[1]: 0.26mm / ~0.01in / ~0.74pt
At a scale of 1:2 these amounts are doubled, while at 2:1 they are halved, and so on.
The “snap” settings are a way of getting an object to move to / align with a nearby grid line. The LO Help pages come under the domain of the LO Web administration and / or LO Documentation teams.
[1] As @Regina points out in a separate answer, the amounts when using the ALT modifier are additionally dependent upon the zoom level. Figures shown are indicative when viewing at 100% zoom.