That first website, which describes the web and how to use it is static and serves information and content to the viewer. It is not particularly attractive and not at all dynamic (a term used to distinguish a web app) but high tech for 1991 standards. Distinguishing a web app from a website might be fastidious, but once you start noting the difference, you will see why it matters. 

A while ago they might have been two vastly different concepts, but today the differences between them are blurred to a point that developers don't make much of the variations anymore. 

Websites mainly focus on what is displayed on the screen and users of websites consume this content without affecting this output. Web applications not only let the user consume content but, allows the user to change what is displayed by deleting and updating data or creating this content. 

To emphasize the difference let's imagine a flight reservation system on an airline website. If the website only allows you to view what flights are available, you have a website. On the other hand, if the website allows you to reserve a seat on a flight, this will be a web app. This example, even if it may be overly simple, shows you how they overlap - you might not want to book a flight but only confirm the departure times. 

Which one should you choose for your business, and does it matter? It's important because the maintenance and development costs differ. To help you decide which is best for you it's best to plan and make the decision on understanding what your business needs are now and what you can foresee for your business in the future. 

• If you only need to advertise your products and services, highlight testimonials, and help establish your brand, a website is the best solution. 
• If you just need a website with some user interaction such as allowing clients or customers to comment on your products or services, then you'll need a web application. 
• Do you want your content and website functionality to be available offline? Does your website need to make use of the device's native features? 

The last point above makes use of a technology we haven't touched on yet - Progressive Web Applications (PWAs). PWAs exist in a world between native applications and web applications and can be seen as web apps on steroids and take advantage of modern web capabilities that provide users and businesses with offline performance, background synchronization and push notifications. 

To sum things up - a web application helps you accomplish specific tasks or automates a particular process, while a website enables you to display yourself or your business online.