Unless you are explicitly referring to Swapbody containers I think you might off in left field. In that Yes there are some containers that aren't commonly supported for transhipment by ship. They are very visually different from Standard Containers. Note these generally are 40+ ft containers....
Nope, just the normal kind. More detail than necessary, but containers destined for truck/rail shipments are now standardized in 48' and 53' foot lengths, and seagoing ones are 40' and 45' in length. Then there are the tractor trailers that have similar features to containers, except they aren't removable from the trailer. Most older models of road/rail containers are visually indistinguishable from normal tractor trailers unless you look at the corners or the trailers and see the tell-tale signs of it being a container, or not. There are exceptions to this. If you are a railfan you may notice the blue Pacer stacktrain containers (you can see similar JB Hunt ones, too). These are similar in appearance to the standard 40' & 45' containers transported via container ships. However these newer containers are in 48' and 53' lengths and don't get loaded onto a ship.
Generally a space going container would be assumed to somewhat more robust than a current Container. One the whole Vacuum thing, which is less of an issue than you are making it out to be. Consider said space going box is going have to be able to support its load in any direction. Plus the load of the surrounding boxes as well. (Note modern Containers strong axis is horizontal with a great deal of their strength being in the corrugated steel walls). As for radiation, that is simple, do it like today, containers that are vulnerable to radiation will be shipped in the inner layers, and I suspect if it is a worry the shipper will take appropriate steps when packing the container as well.
I would also assume a space-rated container to be structurally more robust than one today, but that's pretty reasonable considering containers today aren't built for vacuum standards.
The reason I mentioned three different types is because there would be variations on where you would be using the container, and the simplest version would be the cheapest. A container that is never going to be exposed to space is obviously the cheapest. It means you just need to keep the rain out. No need for a more expensive structure to keep atmosphere in, to protect against radical pressure changes, or the hazards of space. Basically the common slab-sided container you see today. These types of containers would always be carried in pressurized cargo holds.
The space type would obviously be more expensive, but handy if you need to bring it up from a planet or move them around in orbit or a vacuum. The addition of protecting against the rigors of space would require more materials and structural reinforcement.
The final type would be the kind you could strap onto a ship and deliver anywhere in a system. Or leave them on the surface of a vacuum world and not worry about their cargo being damaged by space hazards (within reason of course). Probably not as much call for them, but perhaps. Making them the same size as the other containers means you don't need special equipment to transport them around. Which is the same reason you see specialized types of containers for transporting liquids in frames that mimic the standard container. Being able to deliver that container anywhere makes for great economics. Same as we have today.
Well, yes, but couldn't all container operations be considered a form of LASH operation? In light of some of the Cited Fiction a'la BSG can't you see those ships with containers being 100 dTons?
I would say not. The concept behind the LASH idea was to merge ships and barges with the cargo. The ship takes it across the ocean to a port or river, and then the lighter is directed towards its final water destination and the lighter is unloaded. Containers weren't really big at the time, but in theory you could have loaded containerized cargo on the LASH and moved them that way.
I do see where the LASH concept is getting mixed up. They are very similar in their operations. I suppose the dividing line is that the LASH lighter is actually a vessel, but unpowered, itself. And the big 100 Dton container would not be. There was a similar idea for a modular starship in GURPS that had the primary mover equipped with a J6 drive and as each module was attached the jump went down by one. Each module was self-contained (don't remember if they had thrusters or not though).