The reason the rack is labeled disc mount is because it is designed to go on a disk fork, which has a different spread from V or caliper brakes. I seriously doubt the rack will go through a disc brake mount, but I haven't installed one in a while.
You want something disc-brake compatible. If it says "disc brake mount" it means it's compatible with a disc brake bike. If the rack doesn't mention it's disc brake compatible you can probably still use it but it might take some ingenuity (and a lot of frustration) to rig it up to work well, so it's probably better to get something that specifically mentions disc brake compatibility.
edit: TBH, neither of those racks look particularly good, IMO, but I will defer to someone who has either.
disk brakes usually get in the way of traditional rack mounts. so 'disk racks' typically have legs that arch out to clear the brake . some touring intended bikes may get clever with frame design to allow normal rack compatibility , lookup Surly Troll