tl;dr: what is the difference between 설렁탕 and 설농탕?
They seem to design the same kind of beef-based soup. Is it a difference of meaning (similar albeit different dishes)? Or the same dish in different dialects?
More context: I live in Busan where people usually say that 돼지국밥 (pork-based rice soup) is a typical Busan dish, while 설렁탕 is the Seoul, beef-based version. I enjoy both dishes.
I visited Seoul last week so, following the adage "in Roma, we do as the Romans", I tried to visit a 설렁탕 restaurant. I found one online (신성설농탕 to be precise) in the area of 건국 university (the area I was) under the query "설렁탕" but, to my surprise, the restaurant refered to the dish as 설농탕.
My research: 1. 설렁탕 on Google returns about 2.5 millions results. 2. 설농탕 has "only" 200,000 results. I feel it is too much for a typo, so I am inclined to think it is a local variation.