"Hebrew Roots" is a term that some people apply to anyone who uses Hebrew-ish terminology and believes (or entertains) a set of ideas they don't like. They use it as an insult in the same way that some antisemites use the term "Jew" to apply only to those Jews who act or believe a certain way. Personally, I find the term to have only two useful definitions:
1) A pronomian of non-Jewish heritage who accepts Yeshua (Jesus, Yahusha, etc.) as the Messiah and believes he has been grafted (adopted, joined, etc.) into the chosen nation of Israel.
2) All of definition #1 with the addition of the adoption of Jewish-like traditions, such as tallit-wearing and using Hebrew terms for religious concepts, like Shabbat instead of Sabbath, mashiach instead of messiah, etc.
In either of these definitions, the only difference between "Messianic Judaism" and "Hebrew Roots" is ethnic heritage, although a Messianic Jew is not necessarily pronomian.
Ironically, most of the people who use "Hebrew Roots" as an insult *ARE* Hebrew Roots themselves. Of course, nobody else is obligated to accept my definitions of anything.
I have waffled over the years about whether or not I am "Hebrew Roots", but clearly by this definition I am. Labels are of limited value, though. Being "Hebrew Roots" is a little like being "Christian". It covers a lot of territory.
The Hebrew Roots Movement is a spontaneous, worldwide movement of Christians drawn to the Hebrew Bible, to keep God's commandments as he intended, and to live as Yeshua lived.
Because this movement is spontaneous and counter-cultural, it can be a little chaotic and attracts a lot of people who have an affinity for the fringes. There is no organization or central leadership, so there is a lot of opportunity for charismatic and just plain loud people to claim the stage.
When some people realize they have been taught some lies about the Scriptures, they react very badly, suspecting everything and everyone of trying to deceive them. Ironically, because they are emotionally driven, these people are easy targets for other deceivers. They can become bitter, angry, and even paranoid, making them easily sucked into the absurdities of Sacred Name and Flat Earth. They need true leadership, but they're too afraid to trust anyone. I don't know what to do to help them other than to keep trying to be a calm voice of sanity.
Fortunately, the vast majority of people in the HRM are not bitter and angry. They aren't Sacred Namers or Flat Earthers. They haven't rejected Jesus. They haven't rejected salvation by faith. They haven't rejected Paul. They don't demand that everyone spell God's name exactly like they do. They're good people who are just trying to do the right thing.
Unfortunately, the angry and bitter voices, the prideful and hateful voices are so much louder that they're the only ones that most people remember, and so the entire movement gets painted with that craziness.
Don't be the one holding that brush. Don't be a slanderer of God's people. Don't assume that every disciple of Jesus who has decided to take God's Law (aka Torah) seriously is a lunatic Torah terrorist. Don't violate the two greatest commandments as well as the 3rd, 6th, and 9th of the Ten just because you had a bad experience with a few people who do NOT represent the hundreds of thousands that didn't stick in your memory.
[Apparently, I didn't realize that I had written another article on the same topic with the same title just a month earlier. The question comes up a lot. lol]