Its the generations removed from pure wolf, so F1 (wolf x dog) and F2 (wolfdog x dog), you'd need a DWAL for, and not every county council will licence them.
There are however a lot of multigenerational crossbreed designer breeds meant to look like wolves, ie Utonagans, Tamaskans, Northern Inuits etc.
Then there are the breeds called 'wolfdog' like the Sarloos Wolfdog or the Czech Wolfdog (originating in 1935 and 1955 respectively), which are now a very long way (in the UK at least) from being even a droplet of actual wolf blood and are just rather wolfy racy looking German Shepherds.
They don't need a DWA licence because they're as much wolf as my American cousin is from County Cork...
For some reason people do like to pretend they own a dog with actual wolf content, in the UK, verrrrrrrrry few people do. In the US it is a bit more common because there are more wolves and more dickheads but even then probably 10% of the claimed 'wolf dogs' have any actual wolf content and even fewer still are high content, ie half wolf or more.