I have no idea what the human race is called in the "Galaxy far, far away..." but if I'm not mistaken Mandalorians are just like the human race. I want to know if the Mandalorian race is an offshoot of the human race or actually a unique race with some sort of adaption or something.
Originally, the Mandalorians were the Taung species. They named the first planet they conquered Mandalore, in honor of their leader Mand'alor.
They led several expansion campaigns, and with time other species joined them in their conquests. Eventually the term "Mandalorians" came to describe their war-like culture more than the Taung species.
Later the Taung became extinct around the time of Mandalorian wars.
Wookieepedia has this to say:
Much like the Sith species which gave rise to the Sith Order, the name "Mandalorian" became associated with a multi-species culture of warrior clans, who, regardless of species, adhered to the tenets of the Mandalorians. These Mandalorians, who were mostly baseline Humans, held the legacy of the Taungs in high regard.
The Mandalorians started as the Taung species, hailing from Coruscant. When they finally found the planet Mandalore, their leader (himself named Mandalore) they took it and named that and Concord.
However, nowadays, the Mandalore name implies more of the culture and society than anything else.
The Resol'nare, or Six Actions when translated from Mando'a into Galactic Basic Standard, were the central tenets of Mandalorian life. They consisted of wearing armor, speaking the language, defending oneself and family, raising your children as Mandalorians, contributing to the clan's welfare, and when called upon by the Mand'alor, rallying to their cause.
Tradition dictated that anyone who wished to be considered Mandalorian were to abide by these guidelines and live these actions daily. Mandalorians whom did not follow the Resol'nare were considered to be dar'manda—someone who was ignorant of their Mandalorian heritage and bereft of their Mandalorian soul. The status of dar'manda was widely feared within Mandalorian society due to the belief it meant they were soulless and had no place in the Manda, the Mandalorian afterlife. Before and during the Mandalorian Wars, any and all non-Mandalorians were considered dar'manda and soulless from birth, until they joined the Mandalorians and lived by the Resol'nare. Groups of captured individuals would often be forcibly inducted into Mandalorian culture, and made to swear by the Resol'nare with or without their consent under the threat of death. Such zealotry faded over time as the Mandalorians became a less religious and more secular society.
Young Mandalorian children were taught a rhyme to help them learn the tenets of the Resol'nare, and their parents would explain the cultural significance of each tenet as they grew.
Wookieepedia page for Resol'nare
True, Wookieepedia is not necessarily considered 'canon' but it's as close as we can get here.
If you need further clarification, you can always email Karen Traviss, who wrote and basically created the majority of Mandalorian lore for Star Wars.
The answer to your question will depend on exactly what you mean by "Mandalorian." The term could accurately be used to refer to members of a planet, a system, or a culture.
More broadly, the Mandalorian government also had a presence on various other planets and moons. The planet Mandalore was in the center of the Mandalore sector, comprised of nearly 1,000 planets. Non-human species such as the Phindians were from here.
The Mandalorian culture includes a concept where encountered children of any species in need of assistance are adopted, or at least fostered, as "foundlings."
By creed, until it is of age or reunited with its own kind, you are as its father. - The Armorer, The Mandalorian
These foundlings had Mandalorian affiliation and had the choice to fully join upon adulthood.
Grogu was the most prominent non-human foundling. However, there is no indication given that he was uniquely non-human.
In conclusion, many, if not most, Mandalorians of all definitions were human. There is no evidence that they are genetically unique from any other humans. However, 19% of the planet Mandalore's population, a sizable part of the Mandalorian sector's population, and a non-0% of the Mandalorian culture's population were non-human.