Versus and Horde Siege
Picking up the Core announces you
One object, two modes. In Crucible everyone fights over the Power Core. In Horde Siege it is a delivery job, and the game tells the other two squads exactly who is carrying it.
Crucible (a Versus mode): hold the Power Core in the zone. Three zones win the round, two rounds win the match.
Three zones means the Core has to travel
Ten minutes on the clock, and the zones move. The Core has to move with them, which means the ground you just fought for stops being worth anything the moment you win it.
In Horde Siege the Core is a delivery job
Horde Siege, the co-op mode, uses the same object as cargo, delivered to a R.I.G. (an objective site) or a Supply Cache (a place to refill ammo and change loadout). Picking it up announces you by name to the other two squads. Nothing you equip turns the announcement off, so being seen is the price of the job rather than a mistake you made. All you choose is the moment.
What is not published
Dropping the Core costs progress, not the round: a percentage of your progress at the next checkpoint is lost. The game never states the exact percentage. Numbers quoted elsewhere are unsourced, so none are used here.
The rest of what Horde Siege changed from Gears 5 is in the overview of the mode. It starts with the Fabricator (the machine that built your defenses in Gears 5 Horde) being gone.