No is just for gentiles with no Jewish ancestry. No because of Halacha is for a person who might have Jewish ancestry and might want to or does consider himself Jewish, but admits that he isn't Jewish according to Halacha.
and what about , Yes, but not according to Halacha
That is for someone who considers himself or herself Jewish REGARDLESS of the fact that they are not Jewish Halachically.
What is a non halakhic Jew?
I mean, i can agree if it is someone with a non Jewish mother, jewish father and raised Jewish, but not officially converted. But what if it is someone who has both parents who are Jews, but this person doesn't really practice orthodox Judaism? not shomer shabbat or shomer kashrut? Is he still halakhically a Jew?
I cannot imagine how somebody cannot know this by now.
RULE IS IF MOTHER IS JEWISH OR THEY CONVERTED. THEN JEWISH
so yeah, if they meet those criteria, but eat pork and bacon, then they are still jewish. Just bad jews.
and has to be a proper conversion. Orthodox.
(and to say "non halachic jew" suggests you do not accept halacha). If they are not halachically jewish, then according to halacha, they are not jewish. You might say somebody is ethnically jewish. Or culturally jewish. In halacha that does not make or break somebody being jewish