What is meant by drifts with respect to the stock market?

I think that what you are referring to is Post-Earnings Announcement Drift (PEAD) which is movement in the direction of the earnings announcement after the release. IOW, when a company reports better than expected earnings, share price will drift upward for a few weeks afterward and downward after poor earnings.

Drift simply means steady, gradual movement of some measure, usually towards an equilibrium. The alternative would be a jump, such as where a stock price moves suddenly to an equilibrium price in reaction to something (news, other economic factors, etc.). A drift is more gradual, with the equilibrium being reached over a longer period of time.

There are many types of drifts as you mention, and not all refer to price. "Style drift" is where a mutual fund shifts gradually away from an investment style or objective, for example.

The key is that it's a gradual change rather than a sudden change.