I am looking at bench mats but there are two sizes 23 " and 31" thats width. not sure witch one to buy?

If they are flexible I'd go for the larger one as it can go up the sides a bit if the bench is narrow.  We sometimes get the minimum bench size, but sometimes generous ones depending what the breed is that we are sharing with, or which will be there next day.

I assume these are the widths?

yes . only thing is the mat has a bit that hangs down at the front woth the breed name on. i dont know if it will still hang down if the bench is to small. Dave said get the biggest too . I may bring my tape mesure to manchester lol