And it makes sense - both showed up post-Star Wars, and despite differences from the Empire presented there, both have an Emperor. Neither could really use the term Empire itself, so we have a related term, Imperium. One campaign comes from England as the setting of its Warhammer 40k universe, and the other from America as the setting for its Traveller game.
Warhammer's Imperium first. The Imperium, also called the Imperium of Man or the Imperium of Mankind is a sprawling mass that occupies (but does not dominate) most of the Galaxy. It is ruled with an iron first by the Emperor who is based at Old Terra, or rather by his ministers, since the Emperor is hors de combat from a rebellion some 10,000 years previous, and currently exists on cosmic life support, used to maintain the ability to move through space for the humans and as a buwark against the darkness of chaos, which are the main baddies in the universe. He's a god-sized nightlight.
|The Warhammer Imperium|
The result is pretty much a monoculture. Yeah, the Elf/Eldar are out there, and the forces of chaos, and there are a couple of nonhuman races, but everything is pretty much similar turf for the space marines and their opponents (often other space marines) to pound the ground. But in general, the planets might as well just be one, and exist solely as terrain for Games Workshop miniatures.
The other Imperium is the Third Imperium, though it is also called the Imperium, from GDW's Traveller. It instead occupies a more modest potion of our galactic arm, but its maps are extensively detailed, creating a universe so large that one small segment, usually the Spinward Marches, is enough for an extensive campaign. The Third Imperium has an Emperor, or had one, or has many, as they launched an event where they broke up the empire into smaller but still massive pieces. The center of the Third Imperium was not Earth, but rather Capital (originally Sylea), one of many planets where humans were relocated to by the Ancients, a predecessor race. In fact the Terrans and the Solomani Confederation are considered barbaric latecomers in this universe. Another subgroup of humans are the Zhodani, who are psychic, and, like in the Warhammer Universe, therefore suspect.
|The Traveller Imperium|
Interstellar history is a challenge for the Third Imperium, but they handle it not by freezing time, but rather by engaging in long, looping cycles of empire and collapse, usually in the 16-1800 year range. Given that it was only in the 1200s when the game launched, I had thought of it as an empire past its prime but not falling apart yet. However, more recent product stage a number of Galaxy-shattering events have upended that applecart into smaller groups. Still more recent product then goes back to the glory years of the original.
Of the two, I think I like GDW's Imperium3 over GW's Imperium of Monstrous Men. There is more variety and spaces where the Imperium is not that allows you to set up a campaign, most of them based around taking missions to pay off your ship. Less military, nor merchantile. But both attempt to show worldbuilding at its ultimate ends of taking on the galaxy.