What does the DT in 8A31DT give me?

Dual terminals: each polarity carries both an SAE tapered post and a threaded stud. Clamp-style vehicle cables land on the posts; ring-lug circuits, inverters and accessory feeds bolt to the studs; and a mixed install can use both at once within the battery's ratings. It is the difference between one part number covering a fleet and stocking two variants that differ only in hardware.

Is this a drop-in for any group 31 tray?

Dimensionally, yes: 12.93 by 6.74 inches with 9.40 inches to the terminal tops is the standard group 31 envelope, and the case carries no surprises that fight a hold-down. The checks that remain are electrical, not physical: confirm the charging source lands in the 13.8 to 14.6 volt cycle window or the 13.4 to 13.6 float window at 77°F, and send a label photo of the outgoing unit if you want the match confirmed in writing before ordering.

How do I size the 8A31DT for an inverter load?

Use the rate that matches the discharge speed. An inverter that empties the battery in around five hours works against the 86 Ah figure, not the 105 Ah headline, because capacity falls as discharge current rises in every lead-acid battery. Take the load in amps, pick the closest published rate, and add the reserve margin your application needs; a specialist will run the arithmetic with you on the quote if the duty sits between rates.