Browser desktop mode not really the same as PC desktop Is there anyway to make android browser browse in true desktop mode, i.e. viewing the same layout as a desktop computer?

I know in Firefox, I can click on "request desktop site" in the menu, and some similar function in Chrome.   However, neither of these modes brings me the same experience as I have on a desktop computer.  For example, Gmail has a menu item "filter messages like this", which is missing in "request desktop site" mode, and Similarly for many other web sites.

Some web site provides "full site" button to do this.  But why can't I pretend myself as a desktop computer in the first place? How on earth does the server identify the browser an android browser, even in the "desktop mode"?

Note that this question may seem a duplicate as this question. But I do express the problem in a more general/broader perspective.   

== Update ==

I understand the UI differences such as mouse Vs. touch screen.  What I mean is to emulate a desktop screen mode.  For example, a virtual screen size to mimic a desktop monitor (I can swipe the touch screen to move the view port, and can even enlarge/shrink the view port by two-finger gestures).  A touch emulates mouse left button click.  No mouse right button is acceptable, since most functions should be able to work by just left click.  (Remember Apple Mac desktop might even go with one-button mouse).

The problem is, what they think as "optimize for mobile" might not be what the user think/want, such as removal of some functions.

I don't need "mobile optimize".  Just the browser to mimic desktop one to the maximal extend, and I want to visit the web site in Desktop Mode, as if I connect it by a desktop computer.
There are various ways of creating responsive webpages.

the developer can ask the browser to tell whether it is windows os or android or iPhone or which browser it is etc.

Secondly, most often responsive design is implemented based on the width available to the browser window. To learn more you can search the web or try for yourself as I explain below

In fireFox browser on PC go to menu -> Web Developer -> Toggle tools or press Ctrl + Shift + I



Now click on the button on left of three dots. You can change the size of page to see how it looks on browsers of different sizes.



Hope this helps.