I have read the documentation.  But I don't understand it.  I am a "involuntary DBA".   And I have a hard time following most Microsoft documentation.  I tend to look for forum or blog postings that translate it into a "For Dummies" version.

In my research, looking for an explanation I can follow, I came across this from Paul S. Randal, who has some legit credentials for his expertise.   

https://www.sqlskills.com/blogs/paul/inside-sys-dm_db_index_physical_stats/

In here he says,  
"
The DETAILED mode does two things:

• Calculate fragmentation by doing a LIMITED mode scan
• Calculate all other statistics by reading all pages at every level of the index

"
So, then why would the fragmentation calculations be different between LIMITED and DETAILED?   If you look at the fields I'm pulling, fragmentation is all I'm looking at.