In biblical Hebrew the word מִזְבֵּחַ means altar.
The Torah does not make a distinction between a Jewish and a pagan altar. The Septuagint does. The Septuagint uses 2 Words, βωμός, relating to a pagan altar and θυσιαστήριον, relating to a Jewish altar. For example:
כִּי אֶת־מִזְבְּחֹתָם תִּתֹּצוּן וְאֶת־מַצֵּבֹתָם תְּשַׁבֵּרוּן וְאֶת־אֲשֵׁרָיו תִּכְרֹתוּן
you must tear down their altars, smash their pillars, and cut down their sacred posts
τοὺς βωμοὺς αὐτῶν καθελεῖτε καὶ τὰς στήλας αὐτῶν συντρίψετε καὶ τὰ ἄλση αὐτῶν ἐκκόψετε καὶ τὰ γλυπτὰ τῶν θεῶν αὐτῶν κατακαύσετε ἐν πυρί
Ye shall destroy their altars, and break in pieces their pillars, and ye shall cut down their groves, and the graven images of their gods ye shall burn with fire.
The verse here relates to a pagan altar. The Torah uses the word מִזְבֵּחַ but the Septuagint βωμός. Another example:
וַיִּקַּח מֹשֶׁה חֲצִי הַדָּם וַיָּשֶׂם בָּאַגָּנֹת וַחֲצִי הַדָּם זָרַק עַל־הַמִּזְבֵּחַ
Moses took one part of the blood and put it in basins, and the other part of the blood he dashed against the altar.
λαβὼν δὲ Μωυσῆς τὸ ἥμισυ τοῦ αἵματος ἐνέχεεν εἰς κρατῆρας τὸ δὲ ἥμισυ τοῦ αἵματος προσέχεεν πρὸς τὸ θυσιαστήριον
And Moses took half the blood and poured it into bowls, and half the blood he poured out upon the altar.
The verse relates to a Jewish altar. The Torah uses the word מִזְבֵּחַ but the Septuagint the word θυσιαστήριον. θυσιαστήριον, a neologism in the Greek language, was probably coined by the translators or at least within Jewish Alexandria
The Aramaic targumim similarly distinguished between the Jewish מדבחא and the pagan אגורא (‘heap’ of stones)
In the whole Tanach 22 times מִזְבֵּחַ is translated as βωμός (a pagan altar). But only in Jos 22:10 it is talking about a Jewish altar and not a pagan.
מִזְבֵּחַ is 355 translated as θυσιαστήριον (Jewish altar), but it’s used for a pagan altar 33 times
The Targum makes 51 distinctions between a Jewish and a pagan altar.
It is interesting to note, that in Ex. 32:5 when Aron builds an altar for the golden calf, Onkelos and the Septuagint consider it as a Jewish altar and not a pagan, they translate:
וַחזָא אהרן וּבנָא מַדבְחָא קְדָמוֹהִי וּקרָא אהרן וַאְמַר חַגָא קדם יוי מְחַר׃
And Aharon saw, and builded an altar before it; and Aharon proclaimed and said, A feast shall be held before the Lord tomorrow.
καὶ ἰδὼν Ααρων ᾠκοδόμησεν θυσιαστήριον κατέναντι αὐτοῦ καὶ ἐκήρυξεν Ααρων λέγων ἑορτὴ τοῦ κυρίου αὔριον
And Aaron having seen it built an altar before it, and Aaron made proclamation saying, To-morrow is a feast of the Lord.
 Exod. 34:13; Num. 23:1-2, 4, 14, 29-30; Deut. 7:5; 12:3; Jos. 22:10-11, 16, 19, 23, 26; 2 Chr. 31:1; Isa. 17:8; 27:9; Jer. 11:13
 Jdg. 2:2; 6:25, 28, 30, 32; 1 Ki. 12:33; 13:1-5, 32; 16:32; 18:26; 2 Ki. 11:18; 21:3; 23:12, 15, 17, 20; 2 Chr. 14:2; 23:17; 32:12; 33:15; 34:4; Ezek. 6:6, 13; Hos. 8:11; 10:1-2, 8; 12:12; Amos 3:14
 Exod. 34:13; Deut. 7:5; 12:3; Jdg. 2:2; 6:25, 28, 30-32; 1 Ki. 12:32-33; 13:1-2, 4, 32; 16:32; 18:26; 2 Ki. 11:18; 18:22; 21:3-5; 23:12, 15-17, 20; Isa. 17:8; 27:9; 36:7; Jer. 11:13; 17:1-2; 19:13; 32:29; Ezek. 6:4-6, 13; 16:24, 31, 39; Hos. 4:19; 8:11; 10:1-2, 8; 12:12; Amos 2:8; 3:14; Zeph. 1:5