To the best my knowledge they are the same, meaning the same families of ripening cultures are used and in the same succession to some extent. I believe the the only real difference is how the cultures are applied.
For examples, Limburger and brick cheeses once upon a time the older well cultured cheese, meaning rind, was literally smeared thoroughly onto young cheeses to spread/transfer the ripening culture, and is still done in some places. In this case the surface of the young cheese must have been neutralized to some extent by time or purposeful/accidental introduction of yeasts. Then the star of the show B. linens can take stage and start stinking up the place.
In contrast washed rind cheese is just that. The cheese is either washed/brushed/dunked liberally in or with a weak brine solution (3%ish+) with a combination of ripening cultures i.e. a morge. Or the cheese can be washed with a systematic progression of culture-see the washed rind primer thread.
Washing does have the advantage of being able to keep unwanted molds at bay i.e blue molds. I use this advantage to age one of my blues with my tommes to no detriment to either cheese..............yes it can be done.
Washing and smearing does not have to always lead to the stinky, sticky red/orange archetype we think of. With my complex rind tommes and Stilton type blues I prepare a 3% brine in a shallow tub and on a board set across it gently wash with a wrung dry sponge*my oldest cheeses and the boards they rest on and work my way backwards to my youngest cheese and their boards. I capture this murky and sometimes reeking brine in the tub I am washing from and reuse til I can't stand it.There are a multitude of benefits of having a "real" cave. One being a sustained and controlled environment that is seeded with beneficial ripening cultures that can be harvested indirectly through air flow or directly by mechanical transference.
*On using sponges they can be friend or foe if used improperly. My hygiene protocol (HACCP/GMP's) take it or leave it. Always use a new sponge not one stolen from the kitchen or garage. Wash new sponges natural or synthetic (do you know where it has been or how it was made?) with very warm/hot and very mild soapy water thoroughly to remove any manufacturing residues. Thoroughly rinse and wring with fresh warm flowing water then do it some more. Any residual soap will kill or stunt your wash culture. Wring dry then place in a sanitizer solution 200ppm of regular strength bleach and cool water for 10 min squeezing several times. Wring dry and place on a rack to completely dry. Your sponge is now ready for work. Repeat this process when you are done washing your cheese. I do not store my rags or sponges in my morge. I prefere sponges to rags as my cheese are not nearly as wet and so do not end up sticking to my boards and I do not have to leave my make room to clean them properly.
Hope this is helpful,