The [new] terminology around all Japanese hand tools, and especially Japanese hand saws can be a little confusing when starting out, so I wanted to go over the basic saw models and terms...
At the top level of naming we have Nokogiri. Nokogiri simply translates to "saw" or "Japanese hand saw". This is basically just the word for all hand saws in Japan. Outside of Japan, these saws are usually called pull-saws (due to the saw cutting on the pull stroke of the sawing action) or occasionally razor saws (due to the thickness of the saw itself, they yield an extremely thin kerf), but in the end, they all reference the exact same thing, a Japanese type hand saw.
Next we have the models of hand saw available...
Ryoba Saw - this is a doubled side hand saw, with different teeth configurations on either side of the saw blade. If you don't buy one of our kits (which are great value by the way, cough, just saying), then a Ryoba saw is a great first buy. Double sided for wider applications, this is the most usable Japanese hand saw and one of the best starting points into the world of Japanese hand tools.
Kataba Saw - this is probably the closest hand saw to that we see outside of Japan. Obviously your woodworking applications may be different but I would rate this as the next useful saw after the Ryoba. Made for deep cutting applications, the 2 main types of Kataba saw are the Universal and the Cross-Cut. The cross-cut saw is made for cutting across the grain of timber, while the universal hand saw is used for cutting both with and across the grain. Universal saws are also know as Hybrid Saws, just to make it more complicated. We tend to recommend the universal variant of Kataba saw as this is the most flexible in application.
Dozuki Saw - even though all Japanese saws are very precise, this is next level precision. If you need something for ultra fine joinery, start here. You cannot go as deep with these hand saws due to the wide spine, but this strengthening element of the saw makes it ultra precise, great for dovetail joints and the like.
Flush-Cut Saw - sometimes called a Kugihiki saw (although rare locally) this is a really useful hand saw. I'm always surprised by how many times these saws have been extremely useful. As it says on the tin, cuts flush against another surface thanks to it's ultra flexible blade.
There are more saws variants available but these are the top 4 hand saws we see in use from Japan, the only exception being the Kariwaku Saw. The Kariwaku pull saw is a "carpenters saw" or "carpenters framing saw"... these are long general purpose saws that are great for carpentry work, funny that. Good for builders, gardening/landscaping applications (or during a zombie apocalypse). These also come in a folding saw variants, great for onsite use as they store and travel well in your tool bag.