"Sump" means no more than a "VESSEL" to put the biological, mechanical, or absorbant filter IN there.
This is NOT a definition of what kind of a biological filtration is used.
The same can be told about “canister” filters.
You can put in a sump any kind of a biological filter:
it could be "soaked" (traditional "wet" biofilter, whether "fast" as a canister filter, or a "slow" - as a Hamburger Mattenfilter),
or "wet-dry" (as "trickle filter") - with the extensive contuct of media with air,
or "wet" "fast" fluidized bed filter,
For example you can take a very big in volume "canister" and make a "slow" soaked biological filer inside - Hamburger Mattenfilter.
As you (usually) can not put inside in a canister filter "wet-dry" filter as it is closed and has no contact with air, there is a misunderstanding.
Eheim invented the way to put in a canister “wet-dry” biological filter giving media contact with air (BTW genies).
So really in a sump could be “soaked” biological filter, and in a canister could be “wet-dry” filter.
So both "sump" and "canister" are just vessels to put in there a biological filter. See?
I see like term "refugium" is used when biological filter is a "plant filter", like EcoSystem Aquarium method (no skimmer, no calcium reactor, no massive dosing of chemicals etc) when biological balance is achieved with a Caulerpa (huge algae) growing in one of the compartments of a sump usually called "refugium".
I have made recently a sump for a planted tank
This sump has a compartment inside for “slow” soaked biological/mechanical filter - Hamburger Mattenfilter, and compartment for absorbents – it is a plain internal filter Resun(R) P-1000L with Seachem Purigen inside (needed very rarely).
Hamburger Mattenfilter could be made with Matala(R) mats or "Japanese mats" – approach is absolutely the same - very big surface area giving very slow water movement through every cm3 of media.
For this sump I also made an experimental autonomous universal compartment (removable from a sump) – one size for tanks from 90x45x45 to 180x60x60cm with EstroSieve (plate ~50x60cm cost $200 but it can be cutted for 6 pieces).
This is a best ever filter for a big planted tanks. Simple, cheap, stable, low maintenance.
Takashi Amano used pumice in his sump for a tank 180x120x60cm (see photo 1
, but using Matala® mats is a way better.
One guy from Holland (known for his article about Redfield ratio) have made a sump on a Hamburger Mattenfilter several years ago, but he used a different scheme, no Matala mats, no EstroSieve prefilter, no MISTer PUMP (Hydor ARIO glued to prefilter cap of a Hydor SELTZ II).