According to my book, definition of fringe width can be understood from this figure. According to Byju's, fringe width is the distance between two consecutive bright or dark fringes is called the fringe width: this opposes the definition of fringe width I got from my book.

As the definition of fringe width is wrong, therefore my book got the the formula for fringe width wrong as well: fringe width, $\delta x=\frac{\lambda D}{2a}$[wavelength = lambda, length of separation of screen from slit = D, length of separation of two slits = a]

The above formula was derived from this formula: distance between two consecutive maxima or minima $\Delta x=\frac{\lambda D}{a}$. According to the book, width of a bright fringe and a dark fringe is equal (see figure). If distance between two consecutive maxima or two minima is $\Delta x$ then width of dark fringe or bright fringe or "fringe width" is $\frac{\Delta x}{2}$.

But I think the book is wrong. Width of a bright fringe and a dark fringe is not equal. See this and this. Distance between two consecutive minima or maxima is equal, but the width of a dark fringe and a bright fringe is not equal as is clear from the images.

So, according to my research. the formula $\Delta x=\frac{\lambda D}{a}$ is correct and $\Delta x$ is fringe width, and the formula $\delta x=\frac{\lambda D}{2a}$ is wrong, and $\delta x$ is not fringe width.

Am I correct?