The words Karaite and Qaraite are very confusing and can be used about a few different things:
1) There are some groups of people (whose ancestors came from Central Asia) who have been called Karaite people and the languages of some of these groups of people have also been called Karaite languages. Their ancestors were a type of Christian from the Church of the East sometimes also called Keraites. Many Karaite people say that the word Karaite means "black" in the Turco-Mongol language of their ancestors. That is a traditional Central Asian way to say they were originally from the Northern Turkic tribes.
2) There are also Qaraite people who are mainly Turkic and related to the Karaite people but the Qaraite people mainly converted to Islam. Most people say their name also means "black" but some of these Qaraite people themselves say their name actually comes from an Arabic word for someone good at reading the Quran.
3) There is also a type of Judaism commonly called Karaite Judaism. More accurately it should be spelled in English with a Q not a K, so it should be Qaraite, but Karaite is a more common spelling. In Judaism the word Karaite comes from a Hebrew word meaning "to call out". This Jewish word has a completely different origin from the name used by the Karaite people and Qaraite people. Both words look the same by accident only in English. People who practice Karaite Judaism are called Karaite Jews. In Judaism the term Karaite Language refers to Hebrew.
4) Some Russian Christians -including some of the western groups of the Karaite people- took many ideas from Karaite Judaism but they did not completely give up on Jesus. They became Russian Sabbatarians. They are also called Russian Karaites and Karaite Sabbatarians but there is a big argument about why they are called Karaite. Is it because of their religion? Or is it because some of them descended from the Karaite people or Qaraite people? It seems impossible to know.