Everyone must have different definitions, here's some of my ideas:
Early -- you constantly tweak the research queue to find the right balance between theoretical tech you need and components tech you need.
You carefully desigh sat's and weapon platforms, hopeing they'll hold
You wonder, what's in the next door system, a large, planet with your atmosphere, or the Sergetti and Rage homeworld?
Somewhere in the Mid game -- you have light cruisers with shields, armor, a level 3 direct fire weapon, point defence and combat sensors
you wonder -- Who's holed up in the corner of the map behind the 2 nebulas and a black hole.
Late game is possibly defined as -- monolith III's and robotoid factories on planets waiting for their atmosphere to be converted. Your fleet of dreadnoughts and heavy carriers asks not "Can we wipe out the enemy?" but "How can we wipe out the enemy, creatively?"
"Oh I know, mine their space yard planets, then use engine destroyers to knock out all but one of their engines, now that's funny
"