JBOD will show the drives independently in the operating system. It's just a bunch of disks that use a single connection. SMART and TRIM may or may not work in this mode.
Spanning abstracts the disks from the OS. You'd see something like "J-Micron Disk" (whatever the controller chip is) in device manager rather than "Seagate 1TB Hard Drive ST102023998" or whatever, whether you use a single drive or multiple in this mode. That likely also means the usual limitations of RAID controllers like SMART data not being accessible to the OS, and TRIM commands can't be sent to the drives.
For JBOD mode, according to the manual for this card, the motherboard or add-in card where it's connected has to support the Port Multiplier feature of the SATA spec for this to work. As far as I know, basically no motherboards support the port multiplier feature, but you can buy add-in cards that do. It's doubtful that the board in your DAS supports it. Keep in mind that even if you can make it work, the two drives will be sharing the bandwidth of the single SATA connection.
So you could connect this card in spanning mode in your DAS most likely, but you will have less capability to monitor the health of the drives, and will have no control over which physical drive stores the data. The adapter will simply write to the first drive as long as there is free space, then move on to the other, which means one drive may get a lot more read/write activity than the other. Data that was on one drive may end up getting moved to the other if some data gets deleted from it. Since the TRIM command also can't be sent to the drives, their lifespan and performance will likely suffer greatly (although it could mean that only one drive suffers much while the other doesn't, depending on the load of data). If your DAS is also then applying RAID across more than one of these adapters, it will be even worse (RAID applied over RAID).
RAID0 or RAID1 mode would also likely work in the DAS, and at least with those the data load would be balanced across the drives, but you still would lose SMART and TRIM functionality. You wouldn't gain capacity in RAID1 but would gain redundancy (with no way to know when one of the drives failed so it would be pointless). RAID0 would gain performance but it wouldn't actually be noticeably since the speed of the combined drives would be bottlenecked by passing over the single SATA connection, and at the same time all the data would be lost if one drive failed (which you'd at least notice happening since the DAS's controller would see that the sub-array failed, but you wouldn't know which drive it was).