Right-to-work states still distinguish between firing for cause and a layoff for unemployment purposes. If you just get rid of somebody because you don't like them or whatever, that's legally considered a layoff because they did nothing wrong and thus can still collect unemployment.
If you let somebody go just because you didn't like them but you lied and said it was for performance reasons, they'll have to fight to get unemployment, and they may very well sue you for their troubles. On a similar note, if you do want to fire someone for performance reasons, you better have that lack of performance well documented.
Because of this, a lot of companies don't bother claiming cause: they classify all firings as layoffs and don't contest anyone's unemployment. I worked for a company like that once.
There are some nuances to the terminology. Companies avoid the term "layoff" because it implies that people might be re-hired once the slowdown is over. Growing up near Detroit, I remember layoffs where the status of the laid off workers was specified in the union contract. I have not heard of this kind of layoff in recent times, outside of unionized companies.
Laypeople like me usually reserve "firing" for people who are fired "with cause." When companies fire people "at will," they often use words like "reduction in force."
Perhaps a better way of thinking about it is the consequences of being fired. If you are fired "at will," then you are entitled to things like unemployment compensation, COBRA benefits, etc. If you are fired "with cause," then you lose those benefits.
If an employee is a klunker, they will often wait for business to slow down, fire them "at will," and pay the benefits, to avoid potentially getting sued for false termination.
