The gemara offers possibilities for the definition of מגלה פנים לתורה and אפיקורס. Rashi explains that the language of megaleh panim implies that it is worse than an apikores. Rashi seems to understand that apikores comes from the language of hefker, but megaleh panim is worse because he exhibits tremendous chutzpah against those who study Torah, or creates drashos for the sole purpose of making a farce of the Torah like menashe ben chizkiya.
However, the Rambam defines an apikores as someone who rejects prophesy or rejects Hashem's awareness about people, and defines megaleh panim l'torah as one who does blatant aveiros publicly in a way where he exhibits the chutzpah of not being at all embarrassed about his violations (Teshuva 3:8, 3:11). The kesef mishna already points out that the Rambam seems to have different definitions than the gemara for these terms. The Maharatz Chiyus points out that the Rambam seems to get his definition of megaleh panim l'torah from the yerushalmi who also points to yehoyakim the king of Yehuda who violated aveiros openly. However, the Rambam himself in his commentary on the mishna (immediately before the 13 principles) writes that apikores is an aramaic word for one who is mafkir and degrades the Torah and those who study it. This seems to conform with the gemara definition, and the Rambam doesn't even mention the possibility that rejecting prophesy would also fall under this heading.
Furthermore, the Rambam (Teshuva 3:8) creates a category called a "kofer b'torah" under which he includes: 1. One who denies the Torah being from Hashem including even one pasuk or word. 2. One who rejects that Torah sh'bal peh comes from Hashem. 3. One who says that any mitzvah in the Torah has been retracted or replaced. The Rambam doesn't associate this with being me'galeh panim l'torah. However, in the 13 principles (#8), the Rambam includes anyone who says that even a seemingly irrelevant pasuk is not from Hashem, or one who rejects the divinity of Torah sh'bal peh, and writes that one who takes these positions is a kofer and megaleh panim l'torah. The "kofer" categorization is consistent with the Rambam in the Yad, but the megaleh panim l'torah association isn't consistent with the Rambam in the Yad.