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Learning maseches nozir around daf 35, I encountered two concepts:

היתר מצטרף לאיסור (HML) and טעם כעיקר (TK)

HML

The Gemoro 35b indicates that HML is derived from Bamidbar 6(3)

מִיַּ֤יִן וְשֵׁכָר֙ יַזִּ֔יר חֹ֥מֶץ יַ֛יִן וְחֹ֥מֶץ שֵׁכָ֖ר לֹ֣א יִשְׁתֶּ֑ה וְכָל־מִשְׁרַ֤ת עֲנָבִים֙ לֹ֣א יִשְׁתֶּ֔ה וַעֲנָבִ֛ים לַחִ֥ים וִיבֵשִׁ֖ים לֹ֥א יֹאכֵֽל׃

he shall abstain from wine and any other intoxicant; he shall not drink vinegar of wine or of any other intoxicant, neither shall he drink anything in which grapes have been steeped, nor eat grapes fresh or dried.

This verse indicates that a nazirite gets punished from consuming not only wine and vinegar, but also any food that was soaked in these liquids.

This is because the food which is permitted combines with the (forbidden) liquid to make the requisite quantity.

TK

The Gemoro Pesachim 44b seems to derive the principle of TK from the same possuk,

והאי משרת להכי הוא דאתא האי מיבעי ליה לכדתניא משרת ליתן טעם כעיקר שאם שרה ענבים במים ויש בהן טעם יין חייב מכאן

The word משרת comes to teach that if the nazirite steeped grapes in water and the water took on the taste of wine, the nazirite would be liable to punishment.

So it seems that the concepts are very similar.

What precisely are the differences between היתר מצטרף לאיסור and טעם כעיקר ?

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Rashi in Pesachim defines the two concepts, and stresses the differences between them:

Rashi on Pesachim 43b:

אכל חצי זית חלב וחצי זית בשר בבת אחת אין היתר משלים את שיעור האיסור לחייבו חוץ מאיסורי נזיר שאם אכל חצי זית ענבים וחצי זית לחם בבת אחת חייב

If one eats half a kezayit of chelev and half a kezayit of meat at the same time, the permitted food does not combine with the measure of forbidden food to make him liable, apart from the case of a nazir, where, if he eats half a kezayit of grapes and half a kezayit of bread at the same time, he is liable.

Rashi on Pesachim 44b:

ליתן טעם כעיקר - לעשות טעמו של איסור כעיקרו וממשו:,ויש בהן - במים טעם יין:,חייב - בכזית מהן והא לאו משום היתר מצטרף לאיסור הוא אלא משום דאיתעביד ליה כוליה איסור

To apply ta'am keikar - to equate forbidden taste with the actual food itself. If the water has the taste of wine, he is liable if he drinks a kezayit of it. This is not because of heter mitztaref le-issur, rather that the whole item becomes forbidden.

Note further that the Gemara points out that these are two competing derivations. R. Akiva learns heter mitztaref le-issur and applies it only to nazir. The other Sages learn ta'am ke-ikar and apply the principle to all forbidden foods.

The way Rashi explains the discussion, heter mitztaref le-issur is a specific rule for a nazir that makes you liable for eating a minute amount of forbidden food, as long as your act of eating involved a total amount of a kezayit, seemingly even if the two foodstuffs do not form a mixture. Ta'am ke-ikar, on the other hand, means that in the case of a permitted food suffused with forbidden taste, the entire item is defined as forbidden food, owing to the presence of forbidden taste.

Ba'al HaMaor on the sugya seems to understand heter mitztaref leissur very similarly to Rashi's approach, but he believes that ta'am ke-ikar only applies if you have an entire kezayit of forbidden food dissolved into the permitted food, and one eats the whole kezayit of dissolved forbidden food within kedei achilat p'ras.

This, he stresses, is very different from heter mitztaref le-issur, where eating even half a kezayit of forbidden food together with half a kezayit of permitted food, makes one liable (in the case of nazir).

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