Temurah6: 5
כָּל הָאֲסוּרִים עַל גַּבֵּי הַמִּזְבֵּחַ — וַלְדוֹתֵיהֶן מֻתָּרִים. וְלַד טְרֵפָה — רַבִּי אֱלִיעֶזֶר אוֹמֵר: לֹא יִקְרַב עַל גַבֵּי הַמִּזְבֵּחַ, וַחֲכָמִים אוֹמְרִים: יִקְרַב. רַבִּי חֲנִינָא בֶּן אַנְטִיגְנוֹס אוֹמֵר: כְּשֵׁרָה שֶׁיָּנְקָה מִן הַטְּרֵפָה — פְּסוּלָה מֵעַל גַּבֵּי הַמִּזְבֵּחַ. כָּל הַקֳּדָשִׁים שֶׁנַּעֲשׂוּ טְרֵפָה — אֵין פּוֹדִין אוֹתָם, שֶׁאֵין פּוֹדִים אֶת הַקֳּדָשִׁים לְהַאֲכִילָן לַכְּלָבִים.
[Regarding] all [animals] that are prohibited for the Altar, their offspring are per- mitted. [Regarding] the offspring of a tereifah, R’ Eliezer says: It may not be offered on the Altar. But the Sages say: It [may be] offered.  R’ Chanina the son of Antignos says: A non-tereifah that suckled from a tereifah is disqualified from [being offered] on the Altar.  [Regarding] all consecrated [animals] that be- came tereifos, we may not redeem them, because one may not redeem consecrated [animals] in order to feed them to dogs.
Temurah7: 1
יֵשׁ בְּקָדְשֵׁי מִזְבֵּחַ מַה שֶׁאֵין בְּקָדְשֵׁי בֶדֶק הַבַּיִת, וְיֵשׁ בְּקָדְשֵׁי בֶדֶק הַבַּיִת מַה שֶּׁאֵין בְּקָדְשֵׁי מִזְבֵּחַ, שֶׁקָּדְשֵׁי מִזְבֵּחַ עוֹשִׂים תְּמוּרָה, וְחַיָּבִין עֲלֵיהֶם מִשּׁוּם פִּגּוּל, נוֹתָר, וְטָמֵא, וְלָדָן וַחֲלָבָן אָסוּר לְאַחַר פִּדְיוֹנָם, וְהַשׁוֹחֲטָם בַּחוּץ חַיָּב, וְאֵין נוֹתְנִין מֵהֶם לָאֻמָּנִין בִּשְׂכָרָן, מַה שֶּׁאֵין כֵּן בְּקָדְשֵׁי בֶדֶק הַבָּיִת.
There are [laws pertaining] to items consecrated to the Altar that are not [applicable] to items consecrated for the upkeep of the Temple, and there are [laws pertaining] to items consecrated for the upkeep of the Temple that are not [applicable] to items consecrated to the Altar. Items consecrated to the Altar can produce a temurah, and we are liable on their account for piggul, nossar, and tamei. Their offspring and milk are prohibited after their redemption, one who slaughters them outside [the Temple] is liable, and we do not give of them to craftsmen for their fee. This is not the case with things consecrated for the upkeep of the Temple.