As far as I know, these are order-action. So the unit is attempting to move or assault, but may have been "halted" by fire or threat of heavy fires from seen enemy, stopped to rest, deployed to fire heavy weapons at observed enemy, dug-in in contact with enemy forces etc... the order, and eventual 'task' of the unit remains to complete the movement, but it is not currently doing that.
Dug-in is a little more complex ~ while the first element to halt in a particular location takes the full 'dig-in' period, later arrivals can take advantage of existing works to get into cover much faster... This can reduce casualties dramatically, but will also sometimes halt/slow movement as the 'best' terrain is at the current location, and movement forward increases exposure.
Note that movement is the order type for an attack order for all portions up to the FUP and assault task to the final objective.
Read them as 'We are attempting to Move, and are...' 'We are halted by enemy presence, and will now...' etc.