Its never been explain clearly in the documentations or may be I missed it. But what is the different between Page layouts and Text layouts? Well, both of them defines how your page looks like and if you never work with Text layouts, it is available in Text format tab of Wiki page. So, what are the differences?

Availability

Page Layouts available in publishing page, while Text Layouts available in wiki page. You can find page layouts setting in Page tab of publishing page but you will not be able to find Text layouts in it. On the Wiki page, you will find Text layouts in Text Format tab, but you will not able to find Page Layouts. So, here is the screen shot. Page layouts Text Layouts

Storage

Page layouts areas are backed by different field, while all text layouts areas go to single field. Every time you change your page layouts, you will change to different sets of fields (usually referred as Content types). Every area in page layouts is presentation of a field in the content types. On the other hand, changing text layouts into 2 or more areas will not link to different set of field. All content of wiki page (including different text layouts areas) will be stored into wiki content field.  Page layouts Text layouts  

Customizing

You can customize page layouts by using Designer Manager to convert html design page, or manually edit and insert sharepoint’s html tag. Unfortunately, I have no idea how to customize Text Layouts - so I can say that Text Layouts is very limited in nature. Page Layouts   Text Layouts (undocumented / limited)