Shulchan Aruch Yoreh De'ah 158 (with the commentary of the Shach) provides a very different consequence between the two intentions:
Yoreh Deah 158:1:
וְרוֹעֵי בְּהֵמָה דַּקָּה מִיִּשְׂרָאֵל בְּאֶרֶץ יִשְׂרָאֵל בַּזְּמַן שֶׁהָיוּ רֹב הַשָּׂדוֹת שֶׁל יִשְׂרָאֵל וְכַיּוֹצֵא בָהֶן, אֵין מְסַבְּבִין לָהֶם הַמִּיתָה, וְאָסוּר לְהַצִּילָם אִם נָטוּ לָמוּת... במֶּה דְּבָרִים אֲמוּרִים, בְּיִשְׂרָאֵל בַּעַל עֲבֵרוֹת וְהָעוֹמֵד בְּרִשְׁעוֹ וְשׁוֹנֶה בּוֹ תָּמִיד ... אֲבָל יִשְׂרָאֵל בַּעַל עֲבֵרוֹת, שֶׁאֵינוֹ עוֹמֵד בְּרִשְׁעוֹ תָּמִיד, אֶלָּא עוֹשֶׂה עֲבֵרוֹת לַהֲנָאַת עַצְמוֹ, כְּגוֹן אוֹכֵל נְבֵלוֹת לְתֵאָבוֹן, מִצְוָה לְהַצִּילוֹ וְאָסוּר לַעֲמֹד עַל דָּמוֹ.
...and Jewish shepherds of grazing animals in Israel at a time when most fields in Israel belong to Jews, one does not orchestrate their death but one does not save them from death... when is this true? Regarding a Jew who continues to violate and remains in his wickedness and constantly repeats it... but a Jew who sins, but doesn't constantly remain wicked, just he sins in order to fulfill his desires, such as one who eats un-slaughtered meat for his appetite, it is a mitzvah to save him and forbidden to watch him lose his life.
The Shach there, #3, explains that even the first rule is only by the shepherds, where Chazal made a special decree to deter them from there ways (see there for why). But by a regular thief, one would save them.
However, Yoreh Deah 158:2:
הַמִּינִים, וְהֵם שֶׁעוֹבְדִים לַעֲבוֹדַת כּוֹכָבִים, אוֹ הָעוֹשֶׂה עֲבֵרוֹת לְהַכְעִיס, אֲפִלּוּ אָכַל נְבֵלוֹת אוֹ לָבַשׁ שַׁעַטְנֵז לְהַכְעִיס הֲרֵי זֶה מִין; וְהָאֶפִּיקוֹרְסִים, וְהֵם שֶׁכּוֹפְרִים בַּתּוֹרָה וּבִנְבוּאָה מִיִּשְׂרָאֵל, מִצְוָה לְהָרְגָם. אִם יֵשׁ בְּיָדוֹ כֹּחַ לְהָרְגָם בְּסַיִף, בְּפַרְהֶסְיָא, הוֹרְגוֹ. וְאִם לָאו, יָבֹא בַּעֲלִילוֹת עַד שֶׁיְּסַבֵּב הֲרִיגָתוֹ
Heretics, which are those who serve idols, or do sins [as an act of rejetion] in order to anger [Hashem], even if it is [merely] the eating of un-slaughtered meat or wearing shaatnez to anger, this is a heretic, and apikorsim, which are those who deny the Torah and prophecy among Israel, it is a mitzvah to kill them. If one can do it publically wich a sword, do so. If not, bring it about with some excuse...
The Rambam at the end of his 13 principles in the introduction to Sanhedrin really makes this distinction:
וכאשר יהיו קיימים לאדם כל היסודות הללו ואמונתו בהם אמתית הרי הוא נכנס בכלל ישראל וחובה לאוהבו... ואפילו עשה מה שיכול להיות מן העבירות מחמת תאותו והתגברות יצרו הרע הרי הוא נענש לפי גודל מריו ויש לו חלק. וכאשר יפקפק אדם ביסוד מאלו היסודות הרי זה יצא מן הכלל וכפר בעיקר... וחובה לשנאותו ולהשמידו
When one accepts all of these principles... he is included in the category of "Yisrael" and it is a mitzvah to love him... and even if he does a sin out of desire or the overpowering of his evil inclination, he is punished according to the extent of his rebellion and he has a portion [in the World to Come]. But when one rejects one of these principles, he leaves the category [of Yisrael] and denies everything... and it is an obligation to hate him and obliterate him
Firstly, the Rambam writes that one is punished according to the extent of their rebellion. But more fundamentally, the Rambam defines someone who accepts the system of belief which binds him to Torah and mitzvos (see here for more on that) as being included in Yisrael, and one should love them, and one who rejects that system is out of the category and one is obligated to hate them.
Regarding if one would therefore commit a violation of the first type in order to stop someone else from committing a violation of the second type, there is a very on-point Tosefos in Shabbos 4a s.v. וכי אומרים. The Gemara there says that אין אומרים לאדם חטא כדי שיזכה חברך - we do not tell someone to sin in order that their friend merit (in not sinning). Tosefos, to resolve a conflict with another Gemara, writes that if the sinner is sinning through no fault of yours and unrelated to you, you are not obligated, and are indeed prohibited, from doing a minor sin to save him. Alternatively, Tosefos says that if the sinner is sinning wantonly, you are not obligated, and are indeed prohibited, from doing a different sin to prevent his sin. Both of these lines of reasoning apply to this case, with the conclusion that you would not sin to stop his sin.