(Naniwa no ashi wa Ise no hamaogi;
“What they call ashi in Naniwa is hamaogi in Ise”)
Different places are different – they have different manners, different customs, and even different words for the same things, so be aware. Don’t expect everything to be the same everywhere.
We begin with place name 難波 (Naniwa), an area in Osaka whose name is now read as Nanba, followed by the noun 葦 (ashi), a kind of reed. The associative particle の (no) shows that the ashi “belongs to” Naniwa.
Similarly, the following phrase begins with place name 伊勢 (Ise), a place in Mie prefecture known for the Ise Jingu shrine; the particle の again associates with this place the noun 浜荻 (hamaogi)… which can mean multiple things, including a form of seaside grass, but which in this case refers to the exact same plant as 葦.
These two noun phrases are joined by the particle は (wa), in this case acting as a topic marker and implying that one half of the phrase matches the other.
It’s only natural that this kind of saying would have a number of variations! These range from the very general 所変われば品変わる (tokoro kawareba shina kawaru), “when the place changes, the [physical] things also change,” to the very specific 品川海苔は伊豆の磯餅 (Shinagawa nori wa Izu no isomochi), which seems to be comparing regional specialty foods – in this case, sheets of dried seaweed versus a style of pounded-rice cake.
(“Nyuuyooku-shi ni hikkoshite, hiiroo tte meshi wo tabete miyou to omotte itte mitara, tada no sabumarin sandoicchi datta nda. Amerika mo Naniwa no ashi wa Ise no hamaogi de tabemono no namae ni chihousa ga aru mitai.”)
[“After moving to New York I thought I’d go try this food called a “hero,” but it was just a sub sandwich! It looks like American food has its own regional naming variations, just like Naniwa’s ashi and Ise’s hamaogi.”]