There are some big differences between stand and real life:
1) In the stand, the bike is typically hanging from a support rather than being supported by its wheels. If the wheels are not fully secured in place, this might change their position somewhat.
2) Chain skips and similar events usually happen when the drivetrain is under load; when testing on the stand, the drivetrain is usually NOT under load.
3) A related difference is that things flex when force is applied to them. When you sit on the bike, the frame will flex. When you pedal under hard load (e.g. steep uphill), the cranks will flex. If the flexing is significant, it may alter the relative positions of parts of the bike enough that you see issues.