Our gemara on Amud Beis notes that the sin offering (chattas) is sacrificed in the same location:
וּגְנוּתוֹ בְּקוֹל רָם וְהָאָמַר רַבִּי יוֹחָנָן מִשּׁוּם רַבִּי שִׁמְעוֹן בֶּן יוֹחַי מִפְּנֵי מָה תִּקְּנוּ תְּפִלָּה בְּלַחַשׁ כְּדֵי שֶׁלֹּא לְבַיֵּישׁ אֶת עוֹבְרֵי עֲבֵירָה שֶׁהֲרֵי לֹא חָלַק הַכָּתוּב מָקוֹם בֵּין חַטָּאת לְעוֹלָה
The Gemara asks: But should one really say that which is to his discredit in a loud voice? But didn’t Rabbi Yoḥanan say in the name of Rabbi Shimon bar Yoḥai himself: For what reason did the Sages institute that the Amida prayer should be recited in a whisper? So as not to embarrass transgressors who confess their transgressions during their prayer. There is proof that transgressors should not be embarrassed, as the verse detailing where different offerings are slaughtered does not differentiate between the place where a sin-offering is slaughtered and the place where a burnt-offering is slaughtered, so that it will not be recognized when one is bringing a sin-offering and the sinner will not be embarrassed. This shows that one should also say that which is to his discredit quietly.
The Alshich (Vayikra 6:17) adds to this thought. Actually the Olah offering and the Sin offering are really the same to God; whether we sin or offer him gifts, in the end, we cannot reach him or do anything for him. It is all for us. To God, in one sense, sin and saint are the same. But from Man’s vantage point there IS a difference. An Olah sacrifice is not eaten because it is for acts of omission, impure thoughts and other distancing from God. It is an inaction so it does not require a human action and is fully burned on the altar. A chattas sin-offering is for a sinful deed. Therefore, Man must repair and do action in this world. The Cohen eats from the sin offering, repairing and restoring objects and actions in this world, which had been corrupted and now are brought back into the service of God.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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