^ gamma lids make the buckets water tight so you won't spill any water. Bringing them along ready to go allows for a proper wash of the vehicle. You NEVER want to use those brushes the place provides let alone their soap. The brushes will scratch your finish and who knows what type of soap they're using.
So the buckets with lids allow for the actual washing, the car wash bay allows for the pre-rinse and final rinse before and after the actual washing.