You cannot. You are mixing two different notions and link types.
On your multipost pages (index, monthly and category archives) – you will always ahve exactly what you saw: page/2… /3… /4 etc. E.g. you have 45 posts and your blog is set to display 5 posts when reading > you will have 9 “pages” – it is called the paged view.
On your single post view (after you click on the tiotle=permalink) you have the type of links that navigate between the next-prev single posts, based on their chronology.
These two types of links use different template tags and they are NOT interchangeable.
No, “previous” (in time) means older. Previous always points to the posts the were publish earlier in time; and “next” from that “older moment in the time” comes back – through next – to the present day.
Your problem is you put the labels in the wrong way; see the article in the Codex.