Ignore for a moment that this question is rapidly becoming anachronistic and the items referenced will soon be forgotten. It’s the difference between the two that still has a lot of relevance today.
You used the white pages directory when you knew the name of a person or company and wanted to get their telephone number or address.
You used the yellow page directory when you knew the type of product or service that you wanted but you either didn’t know or weren’t sure of the name that you were looking for.
Today, you use a search engine for both of these purposes. However, what we have found is that many businesses think it sufficient to fulfill only the “white pages function”. This is apparent when a business’ website talks in the first person about “what we do/are/sell/etc.” This type of website ignores its visitors who are looking for a product or service that they need or want.
If the website doesn’t clearly say it the terms the visitor understands that visitor will leave even if they could have found what they wanted. This is similar to the frustrating experience that anyone using the yellow page directory found when they looked up what they wanted only to have the directory tell them that what they were looking for was listed elsewhere.
Every business has the opportunity to optimize their website to being both a “white pages” listing and a “yellow pages” listing. It’s not obvious and it takes the right kind of work to do it correctly.
It’s what we do.