Distance between interference and diffraction fringes In problems related to Interference and Diffraction fringes - I often have encountered phrases like "bright fringes 1.5 mm apart" or "distance between first bright fringe and 4th dark fringe". Fringe is some sort of rectangle not a point.
we can talk about distance between two points not distance between two say, bands.
I think both interference and diffraction fringes are equal width - determined by wavelength, distance between slits and screen and distance between slits or width of one slit.
in one text book - it is mentioned that in diffraction fringe widths are not same where it is same in interference. Is it right?
 A: 
Fringe is some sort of rectangle not a point. we can talk about distance between two points not distance between two say, bands.

I'm not sure what your question is. However, your statements are examples of loose but commonplace language. It would be more accurate to say the shortest distance between adjacent bands, or the spacing between bands.

I think both interference and diffraction fringes are equal width - determined by wavelength, distance between slits and screen and distance between slits or width of one slit.

The geometry of the fringes are determined by all of the variables you've determined. That doesn't mean that the expressions have to be equal. For example, the two expressions $at$ and $at/2$ both depend on $a$ and $t$, but they don't yield the same result.

in one text book - it is mentioned that in diffraction fringe widths are not same where it is same in interference. Is it right?

If click this Google image search, you'll see the closely spaced interference fringes and the wider spaced diffraction envelope. Using a ruler or your fingers, you may be able to answer this question by directly measuring.
If you'd like more info, this link has some more details on both types of fringes.
