The Mishnah uses the word "says" as "says to himself" a way of indicating belief. For instance, "one who says, I will sin and I will return", which is talking about a person who thinks that it's ok to sin with the intent to repent, not someone who literally says those words.
This is also obvious from the context of the Talmudic passage in Sanhedrin 99a that speaks about these things.
But it is not the type of beleif that is generally meant when discussion of religions take place, at least in English. I.e. blind faith - where a person has no first hand information to prove the reality one way or another and only beleives based on whatever they think, or have been taught, is trustworthy.
Concerning (האומר), as the Rambam explained it in the Moreh Hanevuchim 1:36 there is a difference between someone who is decided in their own mind to be fixed in something that is opposite of the reality - someone who is well established in what the reality is yet they set their mind against the reality. (קובעים כדעה) That would normally not be considered beleif, at least not in the religious sense. Again, going by how most westerners address religion and beleif.
Thus, as the Rambam mentions in his commentary on the Mishnah Hullin 1:2 that the (דין) of someone like this, who starts a minut, is different than someone who grew up in it or was fooled by someone else into it. I would assume that from what he described in the Moreh that the danger is that the person who knows the reality and is fixed/set in being opposite to what the truth reality are in most cases they are going to go out and publicize their minut to convince others. There is also the issue that the Rambam also states that a rasha has a place in the world to come, depending on the level of their aveiroth.
וכן כל הרשעים שעוונותיהם מרובין--דנין אותן כפי חטאותיהם, ויש להן חלק לעולם הבא: שכל ישראל יש להן חלק לעולם הבא, אף על פי שחטאו--שנאמר "ועמך כולם צדיקים, לעולם יירשו ארץ" (ישעיהו ס,כא)א
Even in Sanehdrin 99a what is being described is not the same as for example someone who is a (תינוק הנשבה). The person who says they will sin and return is someone who knows the truth and decides to turn away from it. Someone who doesn't beleive in something personally because they only have blind faith to go off or they beleive incorrectly because they don't know any better is not the same thing, especially if they are fully committed do things that they either don't in fully or doubt because they don't know the reality. Thus, that is not the same as what is often termed as "religous beleif."
That is what I mean. I hope that I wrote that so it is clear.