The idea behind these two alert actions is to assign the alert to an operator to work on. The operator then 'accepts' it and works on it.
If you assign an alert to yourself then you automatically accept it. The colour in the left most alertId column is just a quick indicator of acceptance. CBA ( Colour By Assignment ) also shows services as purple when all alerts associated to a service are assigned.
There is also a supervisor Acknowledge/Deacknowledge but these are just additional flags and are not really used by anything.