RFC 7231 - Hypertext Transfer Protocol (HTTP/1.1):User-Agent Semantics and Content

Wed interactions between servers (e.g. Google) and clients or user agents (e.g your smart phone or computer) are defined by the application level Hypertext Transfer Protocol (HTTP).

When you send a request for a web page the browser includes information about your browser (user agent) in the http header. This includes:
User Agent: Information about the version of your Operating System (OS) [ Windows, Mac OS X, iOS, Android, ...] and browser [Chrome, Internet Explorer, Firefox, Safari, ...]
In addition to name and version it includes the type of rendering engine it uses [Trident, Gecko, Presto, Blink or WebKit.] Firefox user agent string reference - HTTP

Terms:
Rendering Agent: Trident, Gecko, Presto, Blink or WebKit.

Mozilla/5.0 is the general token that says the browser is Mozilla compatible, and is common to almost every browser today.

platform describes the native platform the browser is running on (e.g. Windows, Mac, Linux or Android), and whether or not it's a mobile phone. Firefox OS phones simply say "Mobile"; the web is the platform. Note that platform can consist of multiple "; "-separated tokens. See below for further details and examples.

rv:geckoversion indicates the release version of Gecko (such as "17.0"). In recent browsers, geckoversion is the same as firefoxversion.

Firefox/firefoxversion indicates the browser is Firefox, and provides the version (such as "17.0").

Phone UA:
Mozilla/5.0 (Linux; ; ) AppleWebKit/ (KHTML, like Gecko) Chrome/ Mobile Safari/

Tablet UA:
Mozilla/5.0 (Linux; ; ) AppleWebKit/(KHTML, like Gecko) Chrome/ Safari/

Galaxy Nexus: Chrome
Mozilla/5.0 (Linux; Android 4.0.4; Galaxy Nexus Build/IMM76B) AppleWebKit/535.19 (KHTML, like Gecko) Chrome/18.0.1025.133 Mobile Safari/535.19

Windows Operating System  Version number and Name
Version         Name
Windows;        Windows 98 or 95
Windows NT 4.0; Windows NT
Windows NT 5.0; Windows 2000
Windows NT 5.1; Windows XP
Windows NT 5.1.1; Windows XP
Windows NT 5.2; Windows Home Server
PWindows NT 6.0; Windows Vista
Windows NT 6.1; Windows 7
Windows NT 6.2; Windows 8
Windows NT 6.3; Windows 8.1
Windows NT 6.4; Windows 10 (Depreciated)
Windows NT 10.0; Windows 10
Windows NT 10.10;

My Tests:

Windows 7 IE
Mozilla/5.0 (Windows NT 6.1; WOW64; Trident/7.0; SLCC2; .NET CLR 2.0.50727; .NET CLR 3.5.30729; .NET CLR 3.0.30729; Media Center PC 6.0; .NET4.0C; GWX:QUALIFIED; .NET4.0E; rv:11.0) like Gecko

Windows 7 Chrome
Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/48.0.2564.97 Safari/537.36

Windows 7 Firefox
Mozilla/5.0 (Windows NT 6.1; WOW64; rv:44.0) Gecko/20100101 Firefox/44.0

Windows 10 Edge
Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/46.0.2486.0 Safari/537.36 Edge/13.10586

MacBook Pro Chrome
Mozilla/5.0 (Macintosh; Intel Mac OS X 10_11_3) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/47.0.2526.111 Safari/537.36

MacBook Pro Chromium
Mozilla/5.0 (Macintosh; Intel Mac OS X 10_11_3) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/47.0.2508.0 Safari/537.36

MacBook Pro Safari
Mozilla/5.0 (Macintosh; Intel Mac OS X 10_11_3) AppleWebKit/601.4.4 (KHTML, like Gecko) Version/9.0.3 Safari/601.4.4

Macbook Pro Firefox
Mozilla/5.0 (Macintosh; Intel Mac OS X 10.11; rv:44.0) Gecko/20100101 Firefox/44.0

LG G Pad tablet Chrome
Mozilla/5.0 (Linux; Android 4.4.2; VK810 4G Build/KDT491.VK81022B) AppleWebkit/535.19 (KHTML, like Gecko) Chrome/47.0.1025.83 Safari/537.19 ...

LG G Pad tablet Dolphin
Mozilla/5.0 (Linux; U; Android 4.4.2; en-us; VK810 4G Build/KDT491.VK81022B) AppleWebkit/535.19 (KHTML, like Gecko) Version/4.0 Safari/537.16 Chrome/33.0.0.0

Nexus 7 tablet Chrome
Mozilla/5.0 (Linux; Android 5.1.1; Nexus 7 Build/LMY47V)AppleWebKit/537.36 (KHTML, like Gecko) Chrome/47.0.2526.83 Safari/537.36

iPhone 5S Safari
Mozilla/5.0 (iPhone; CPU iPhone OS 9_2_1 like Mac OS X) AppleWebKit/601.1.46 (KHTML, like Gecko) Version/9.0 Mobile/13D15 Safari/601.1

iPhone 5s Dolphin
Mozilla/5.0 (iPhone; CPU iPhone OS 9_2_1 like Mac OS X) AppleWebKit/601.1.46.60.1 (KHTML, like Gecko) Version/6.0 Mobile/10A523 Safari/8536.25

iPhone 5s Chrome
Mozilla/5.0 (iPhone; CPU iPhone OS 9_2_1 like Mac OS X) AppleWebKit/601.1.46 (KHTML, like Gecko) CriOS/48.0.2564.87 Mobile/13D15 Safari/601.1.46

Android phone
Mozilla/5.0 (Linux; ; ) AppleWebKit/ (KHTML, like Gecko) Chrome/ Mobile Safari/

Other User Agent lists:Browsing Windows User agents : What Is My Browser
Most Common User Agents - Tech Blog (wh)

Links:
User-Agents.me - User agent string analysis
JavaScript: OS detection
How to detect my browser version and operating system using JavaScript? - Stack Overflow Understanding user-agent strings (Internet Explorer)
Latest user agent strings . gorhill/uMatrix Wiki . GitHub
Mobile Browser ID Strings (a.k.a. User Agent ID)
Browsers