Boot cut means a slightly flared leg (think a very very subtle bell bottom) so that they fit over cowboy or work boots easier.
Relaxed fit means it's made a little bigger in the seat and thighs compared to the same size in a regular fit. The lines/silhouette aren't as clean/nice, but it's comfier; which is why it's called relaxed fit.
You should default to assuming anything Fox says is untrue without a second source to verify. Because legally they can just say whatever they want and aren't beholden to any type of journalistic standards because they aren't news.
They have no more credibility than a random social media user.