Hand saws are very old technology. Here are some key differences.

1. Japanese flush cut, or any other flush cut saw will have no tooth "set" so will not mar surfaces
2. A saw not sold as a "flush cut" saw will have tooth set and will mar surfaces
3. Some hand saws are stiffer than others and are made for specific purposes, like cutting dovetails
4. Some saws cut on the push stroke, some cut on the pull stroke

My recommendation is to get a flexible flush cut saw and a rigid blade cross cut saw. You will find many uses for both saws and may purchase additional saws over time. I use the flexible flush cut saw frequently on many projects.