Id assume, that the differences between minor lockdown, major lockdown and total lockdown (quarantine) are the same as for minor/major/total in every other context too. Minor x = a small quantity of all possible x, major x = a large quantity of all possible x, total x = all of all possible x. X in the given context would then be something like "measures to achieve isolation (on different levels) to decrease infection rate".

Practical example: Minor lockdown could be shutting down public places and canceling events that attract large crowds (>1000 people). Major lockdown could be shutting down all public places and closing borders. Total lockdown would be complete isolation of all individual people, as far as possible, for example via curfews and special protocols like for example (as they did in China) mailmen dropping packages on the doorstep instead of handing them over to you, and similar protocol changes to avoid direct contact between people. — And these three steps are in fact exactly what has been done or is in the process of being implemented right now in many countries.