While english isn't my native language as well, I think "show" and "display" are both used in a very similar context of "revealing" more information for a specific object.
Revealing information on the other hand is one of the most frequently needed features for almost every UI. That said, my experience is that well designed intuitive UIs don't need to make use of the terms (= labels) "show" or "display" at all by instead providing standardized link decoration (colors, boxes, hovers...) or just buttons that are used in conjunction with the particular placeholder information leading to the more detailed information. For example guess a list of user names that can be directly clicked to let their profile appear.
When referring to information that is primarily a 2nd-choice click or - explained differently: loosely coupled with the current context (or content, task, whatever) - it may be the better way to extend the labels information with what's going to be shown, like
Show Product Details,
Display User Stats or just
Show All Friends.