The label format decides how much desk space your printer really needs and whether a roll will physically fit. The short answer: fanfold is simplest for external-feed printers; rolls make sense when the printer holds them inside.
The difference in one picture
Illustrative diagram, not to scale. Fanfold stacks sit behind external-feed printers; rolls need a holder or an internal roll bay.
Fanfold labels are folded into a flat stack at the perforations. The stack sits behind (or under) the printer and feeds through a slot.
Rolls are wound on a cardboard core. They sit on an external holder or inside the printer's roll bay.
Which printers take which
Printer
Fanfold
Rolls
Rollo Wireless / Rollo USB
Yes
External holder
MUNBYN P941U
Sold bundled with fanfold labels
External
MUNBYN RW403B
Not stated on the product page
Not stated
Phomemo 241BT
Yes (fanfold test labels included)
External
Zebra ZD421d / ZD220d
Yes (rear feed)
Inside, up to 5.00 in OD
iDPRT SP410, Arkscan 2054A-LAN, POLONO PL60
Yes
Up to 5 in OD
DYMO LabelWriter, Brother QL
No—proprietary rolls only
Maker's rolls
Desk space (approximate)
A 4x6 fanfold stack occupies a 4 × 6 in patch behind the printer. With an external-feed printer that's about 4 in deep, plan roughly 11–12 in of depth including the paper path.
Rollo's roll holder is 9 × 6 × 4.5 in assembled, so an external roll takes a similar depth—plus the holder hardware.
Printers with an internal roll bay (Zebra, for example, at about 8.7 × 7.0 in) need no extra space for rolls.
Assumptions: stack or holder placed directly behind the printer, labels feeding straight.
When to choose each
Choose fanfold if your printer feeds from outside, your desk is shallow but you can leave a gap behind the printer, or you want to avoid core and diameter questions.
Choose rolls if your printer loads them inside (Zebra, iDPRT, Arkscan, POLONO) or you already own a holder. Check the core size and outer diameter against the printer's limits—see label core size and roll diameter.