[UPDATE: Though the original map, available here, shows changes each year, I can't seem to make that work here, so I've just included the static 1986 and 2019 maps for now; working on trying to make the dynamic map work.]
"Unrestricted" means that, generally speaking, any law-abiding adult can carry a gun concealed in public places without a license. (This used to be so only in Vermont; many people, I've found, are surprised by that being the one state.)
"Shall-issue" means that any law-abiding adult (in some states, limited to over-21-year-olds) can get a license to carry concealed, and the government has minimum discretion to deny that license.
"May-issue" means that the government can choose whether to give people concealed carry licenses. (This may vary sharply from county to country or city to city in the state.)
"No-issue" means that concealed carry is categorically forbidden to ordinary citizens (with some exceptions for government employees and perhaps some private security professionals).
From the Radical Gun Nuttery! site, but despite the name (either of that site or of this one), the data seems pretty accurate. You can agree or disagree on whether the change has been a good idea, of course, but it's an important reality to keep in mind when thinking about the shape of modern American gun policy.