Does the term "page" have the same meaning in DBMS and OS jargons?
Does the term page have the same meaning in DBMS and in OS?


Generically, yes. The term PAGE is a generic for the smallest allocate-able unit of space. In SQL Server, for example, pages are a fixed size and have historically been 4k and 8k, depending on version (not counting Large Pages which are virtual memory and not database structures) and in Windows pages can be a multitude of sizes depending on options and underlying hardware.


  Assume page has the same meaning in DBMS and OS, why do we specify the NSM and PAX only in DBMS? Can this page format be portable to OS?


I didn't read the entire paper because it also overloads the same term. Note that the hardware and underlying OS may change what a PAGE size is but doesn't change the generic meaning. Its use is quite overloaded and TBH you can make whatever you want in your own OS.

This is a little too generic and high level to really "answer" per se, and the "answers" are going to be hardware and software dependent and specific. You might want to narrow your focus a bit and ask a much more pointed question as this is extremely wide IMHO.

Edit:

You also mention SSD's, which also have a unit of PAGE which depends on (sarcasm) shockingly enough the storage controller and firmware. Some SSD's use pages of 1MB or more, some smaller.

Normally when we're talking about "Low Level Cache" it's the data or code caches which are generally referred to as lines or segments and not pages.


  Maybe an additional question. Where and how can I find the documentation or implementation of page size or page format from a SQL server? Any particular DBMS or SQL server will make me happy.


SQL Server documents the architecture here. This is fixed and cannot be changed.

Windows page size (not to be confused with a paging file) can be found by calling GetSystemInfo (Windows API) which will populate a _SYSTEM_INFO structure which has a member called dwPageSize that will tell you the current page size for the system - this should all still be 4k at the time of this writing.