For men, charedi means an Orthodox Jew who wears a black hat or at least a white shirt with a black velvet kippah. For women, it means either being married to a man who fits that description, or for unmarried women, identifying with a charedi community (Yeshivish or Chassidic). Often, for women it also means having somewhat stricter tzniut standards (ie, always wearing tights, longer skirts, etc.)
For men, Modern Orthodox just means someone who belongs to an Orthodox shul, and identifies as Orthodox, but doesn’t wear a charedi uniform. (Not all who belong to Orthodox shuls are Orthodox.) For women, Modern Orthodox means being married to one of these men, or for single women, considering themselves a part of the MO community.
In Israel, if you belong to an Orthodox shul but don’t wear the charedi uniform then you’re dati leumi, national religious (unless you’re not very nationalistic, then you might use the term modern Orthodox).
There are many other dimensions of the charedi/MO definition (chumros, mysticism/rationalism, hashkafa related to israel, careers, education, science, da’as torah, feminism, etc.) but since the most visible thing is clothing (and which shul you belong to), that’s the main thing people will use to put you in a category. When you get beyond the clothing, it’s all mixed up and many people will look MO in one dimension and charedi in another.