What are the differences between different Denoiser options built into Blender?

Question

As far as I know, Blender seems to have three denoisers.

1. The default denoising feature in the view layer tab
2. The denoising feature displayed in the view layer tab when optix is enabled
3. The denoise node in compositor (Intel Open Image Denoise)

Questions :

1. Are the Optix view layer denoiser and compositor denoiser nodes the same technology?
2. If all three denoisers are different, I am curious about the name of the algorithm they are using.

Answer 1

All denoise options in Blender are based on different research efforts to speed up path tracing.

Denoising Filter for Cycles

is an implementation exclusively for Cycles by Lucas Stockner during Summer of Code 2016 combining different papers about denoising around 2015:

...this proposal is about having a denoiser right in Cycles - where all the additional information (like feature passes and variance info) is available and can be used to produce results that are far better than general image denoising, often allowing to cut render times by 75% or more.

NVIDIA® OptiX™ AI-Accelerated Denoiser

is a research effort on top of OptiX a GPU library which requires a graphics card supporting CUDA. The Paper was published at SIGGRAPH 2017 and can be found here:

It uses GPU-accelerated artificial intelligence to dramatically reduce the time to render a high fidelity image that is visually noiseless.

Intel® Open Image Denoise

is a library build on top of DNNL (a CPU libary for deep learning applications) published in 2018:

Intel Open Image Denoise internally builds on top of Intel® Deep Neural Network Library (DNNL), and automatically exploits modern instruction sets like Intel SSE4, AVX2, and AVX-512 to achieve high denoising performance. A CPU with support for at least SSE4.1 is required to run Intel Open Image Denoise.

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Related: Which denoiser is better?