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What is the difference between Selenium Webdriver and GeckoDriver?

I use Selenium every 5 years or so and everytime it has changed beyond recognition. I just started a new Selenium project, googled some quickstart guides such as https://www.toolsqa.com/selenium-webdriver/run-selenium-test/ (written in September 2020) and https://www.guru99.com/first-webdriver-script.html (© 2020) and both seem to use WebDriver, e.g., by initiating their examples with WebDriver driver = new FirefoxDriver(); although the latter has a disclaimer saying that from Firefox 35 (I have 82) and up you should use Geckodriver.
I use Selenium for Java 3.141.59 downloaded from https://www.selenium.dev/downloads/ but it only has two references to Geckodriver (at least that is all that is displayed when it enter Ge and autocomplete in my IDE), GeckoDriverInfo and GeckoDriverService (as a comparison, there are nine references to WebDriver).
I have read the information here https://github.com/mozilla/geckodriver but it didn't make me any wiser, nor did https://en.wikipedia.org/wiki/Selenium_(software)#Selenium_WebDriver (Geckodriver isn't even mentioned on this Wikipedia page).
What is the difference between Webdriver and Geckodriver?
Why, if one download the newest/current version of everything, isn't Geckodriver included if that is the recommended tool since several (?) years?
Why are guides that are written recently use Webdriver if Geckodriver is the way to go?
I think I have done a reasonably amount of research before asking this question but feel free to suggest improvements because I am genuinely confused.

WebDriver is a specification. It defines the way how UI interfaces can be automated. GeckoDriver is the implementation of such specification - it is the WebDriver implementation for Firefox browser.
So basically a WebDriver is a server that exposes REST API to one side and that knows how to control browser on another side.
Here is short explanation of E2E flow (for Firefox and Java):
You download Selenium java library. It provides Java client for interacting with web drivers
You download GeckoDriver
In your Java code you call WebDriver driver = new FirefoxDriver();
Selenium library starts GeckoDriver executable in OS native manner
In your Java code you call driver.get("http://my.url")
Selenium library forms REST call to the server that is started with GeckoDriver. It invokes the endpoint according to this section of specification.
GeckoDriver then translates this command to somewhat that Firefox understands so that the browser navigates to required page.
So basically you need 3 things to make everything work:
Selenium Java library that is basically a Java client for WebDriver REST API
GeckoDriver (that implements REST API according to WebDriver specification and translates it to commands which Firefox browse can understand)
Firefox browser

webdriver, is the parent of ChromeDriver ( from chrome ), GeckoDriver ( FireFox ), IEDriver and RemoteDriver. Possibly even more if they are supported. So, the GeckoDriver is used to control a FireFox Browser instance, but it implements the methods mentioned in the WebDriver interface.
GeckoDriver is not included as it is specific to FireFox only, other users may want to use other browsers.
To keep the flexibility of swapping out the implementations for different browsers. :)

Reason behind adding HTML Unit Driver in Selenium 3.0.1

As suggested in the below link, selenium has removed HTMLUnitDriver from selenium distribution as per its evolution strategy.
https://github.com/SeleniumHQ/selenium/issues/2381
While working on Selenium 3.0.1, i have found that HTMLUnitDriver is again distributed with Selenium server.
Can any one explain why again the HTML Unit driver is added as part of selenium server in Selenium 3. I have checked in Selenium 3.0.1 and Selenium 3.0.0.beta-2 . I did not check in the earlier betas of selenium 3.
The addition the browser driver in selenium distribution collides with the selenium evolution strategy that the browser driver need to be separated from selenium distribution. Can anyone tell me why this is added even if it is aganist the selenium evolution strategy?

Java Selenium WebDriver with Yandex

At the moment, I use Firefox as browser for my Java Application with Selenium. But Firefox is slow.
Is it possible to use Yandex as browser? Didn't find anything in Google. Does Selenium supports Yandex? For Chrome I need the .exe for using Chrome as browser. Is this possible with Yandex?

From what I recall, there is no WebDriver for the Yandex ("Яндекс") browser. In other words, there is no way to automate this browser through selenium.
Also, there are some performance tips and further links here:
Selenium WebDriver works but SLOW (Java)

Yandex browser can work with Selenium WebDriver using Operadriver.
System.setProperty("webdriver.opera.driver", "C:\\Users\\User\\IdeaProjects\\testselenium\\drivers\\operadriver.exe");
OperaOptions options = new OperaOptions();
options.setBinary("C:\\Users\\User\\AppData\\Local\\Yandex\\YandexBrowser\\Application\\browser.exe");
WebDriver driver = new OperaDriver(options);
driver.get("https://docs.seleniumhq.org");

This might be what you are looking for ( 4 years later :) ):
https://github.com/yandex/YandexDriver

How to run headless mode in java

I am running test in java selenium test using firefox/chrome driver
I want to run the test in background.
In ruby, i use this gem
https://rubygems.org/gems/headless
How to do in java?

There is a new Firefox headless mode https://developer.mozilla.org/en-US/Firefox/Headless_mode
There is an example of how to use it in Node.js
One would think that would translate over to Java quite well. I'm going to give it a shot.

Other option is using the HtmlUnitDriver which based on HtmlUnit project which "GUI less browser".
//create webdriver
WebDriver driver = new HtmlUnitDriver();

Is there a easiest way to migrate Selenium 1.0 code to WebDriver?

I am having old test automation framework developed using Selenium 1.0 and now wants to migrate my code to WebDriver.
Is there any easiest method to do this migration?
I have overridden most of the methods such as type, click, getText, getSelectedLabel, assert etc etc. I see the only method is to re-write all methods again from scratch, I have already started this process but If I continue with the same method It will take many days for me.
Please suggest if anyone has any better approach.
Thanks in advance.

They are completely different technologies. There is no way to migrate them over to selenium 2 per se.
Luckily, the recent Selenium releases have implemented what's called "WebDriver Backed Selenium" so technically if you are using those tests, it's implicitly running them "as" WebDriver tests.
Other than that, no, there is no easy way.
I had the same issue - we are migrating our entire regression suite over to S2 now :)

In the Webdriver documentation, they explain a method to start migrating from Selenium RC to Selenium WebDriver.
Basically, is creating the selenium object like this:
WebDriver driver = new FirefoxDriver();
Selenium selenium = new WebDriverBackedSelenium(driver, "http://www.yoursite.com");
the main problem with this migration (instead of changing the whole code) is the wait for page to load. As they say, the command WaitForPageToLoad returns too soon. The getEval is another command that you have to change.
I think that the best approach is to make functions with the main commands that differs from Selenium RC to Selenium WebDriver, and, once everything is "working" keep modifying your code until no Selenium RC is present. This is how we did the migration, and we had lots of lines of code.
This is the link, where they explain how to start:
http://www.seleniumhq.org/docs/appendix_migrating_from_rc_to_webdriver.jsp#migrating-to-webdriver-reference