An SOC is a shipper-owned container: a box that belongs to you rather than to the shipping line. A COC, a carrier-owned container, is borrowed for one move and returned. Everything sold on this site is SOC. The practical difference is that a COC comes with a clock attached to it and an SOC does not, and that an SOC is an asset on your side of the transaction.
When you book freight in a carrier's container, the container is theirs. You get free time at each end, and past it the carrier charges demurrage while the box sits inside the terminal and detention while it is out at your premises. Those charges exist to get their equipment back into circulation.
An SOC is your equipment. There is nothing to return, so the carrier's clocks do not apply to it. You book the slot rather than the box, and the box stays yours when the cargo comes out.
Three things, mostly. You can hold the container as long as the work requires, whether that is a storage yard, a site office conversion or a slow-moving export lane. You can position equipment onto lanes where carrier boxes are scarce or expensive, which is why forwarders and NVOCCs run owned-box programs. And you hold a resale asset rather than a rental cost.
For conversion and modular builders the point is simpler still: you cannot cut doors into somebody else's container.
Owning the box removes the carrier's demurrage and detention. It does not remove terminal storage tariffs, which the terminal charges for ground it occupies regardless of who owns the unit. It does not remove the need to book slots, and on some lanes carriers price an SOC slot differently from a COC slot.
It also does not remove maintenance. A COC goes back to a depot that repairs it. Your unit is yours to inspect and keep in condition, which for a new-build is a long way off but is worth planning for.
Owned-box export programs on thin or imbalanced lanes; storage and site use where the box never moves again; conversion into offices, workshops, retail units and housing; and reseller inventory, where the container is the product rather than the packaging.
New-build and one-trip units are the usual starting point for all four, because the working life ahead of the box is what you are actually buying. The terms used here are defined on the terminology page.