Is NMN the same as vitamin b3, niacin, NA nicotinic acid? Does Nam nicotinamide or NR nicotinamide riboside do the same job?

NMN (Nicotinamide Mononucleotide), Vitamin B3 (niacin, NA, Nicotinic Acid), Nam (Nicotinamide) and NR (Nicotinamide Riboside are all different.

The aim of these molecules is boosting Nicotinamide adenine dinucleotide (NAD+) levels.

NAD+ levels naturally decline as the body ages [14], by up to 50% in human skin tissue by the age of 40-60[15].

The below chart shows the NAD+ biosynthesis pathways:

Source - Metabolic aspects of neuronal degeneration: From a NAD+ point of view.

Supplementing with NAD+ itself is not an option to boost NAD+ levels, because it is too big to readily cross cell membranes to enter cells, and therefore would be unable to positively affect metabolism [23].

Vitamin B3 (niacin, NA, Nicotinic Acid)

Niacin, Vitamin B3, or NA (Nicotinic Acid) is able to increase NAD+ levels, but not universally - it does not act as a precursor to NAD+ in important areas such as the brain, skeletal muscle or neurons.
It also often leads to severe flushing, as nicotinic acid binds to the GPR109A receptor[1,2].
In order to be converted to NAD+ by the body, vitamin b3 or niacin or NA (nicotinic acid) is converted to NaMN ( nicotinic acid mononucleotide), and then to NaAD ( Nicotinic acid adenine dinucleotide), and then to NAD+.

NR (Nicotinamide Riboside)

Nicotinamide Riboside is converted to NMN by phosphorylation with the help of nicotinamide riboside kinase (NRK1 and NRK2)[3]. The NMN formed is then enzymatically converted to NAD+.

Nam (Nicotinamide)

Nicotinamide is converted to NMN by the body [4], which is then enzymatically converted to NAD+.

NMN (Nicotinamide Mononucleotide)

NMN is enzymatically converted to NAD+ by the body.
Supplementing with NMN, a precursor to NAD+, has been shown to increase NAD+ levels in mice [3], and is expected to show increased NAD+ levels in humans when clinical trials are completed, as other NAD+ precursors have done[29,30].
Multiple human trials are currently in progress [10,11,31], with NMN at least appearing to be safe for humans to consume, and preliminary results are said to be promising[12].