"Display" can mean a way to proudly show something or to put it in a place (for example, a showcase) for all to see. The purpose of the owner is to let other people be aware of it. So, you can consider that "Display" is more static and passively.

Display有点自豪的展示的意思。展示的目的是为了告知他人，引起他人的注意。通常隐含着被动展示的意思，因为有可能他人不会注意。

Examples:

Many colorful clothes are displayed in the showcase.

展示柜里摆放着很多鲜艳的衣服。

"Show" is the more commonly used word, you could show someone a car or show people a picture on your smart phone. "Show" is more active and dynamic. For example, if I'm showing you a book, I'm holding your attention to it, but if I'm displaying it, I have just set it out for people to observe passively.

It is also used to refer television programs, for example, a TV show.

In most situations on the internet for a website, "show" would be always the best term to use. There is no reason to use "display" instead of "show" when you are talking about something visible on a website.

Show使用的场合更多更普遍。隐含着主动展示，吸引他人注意力的意思。比如，当我给他人show一本书的时候，我想达到的目的是把对方的注意力吸引过来。

Show也用来表达电视节目。”秀” 就是Show的音译。

Examples:

It's time to watch the popular TV show right now.

到了看那个很受欢迎的电视节目的时间了。

Let me show you how this machine works.

我来给你演示这台机器是如何工作的。

The web page will show you how to submit your request in detail.

那个网页将详细的告诉你如何提交你的请求。