The two terms seem to mean the same thing, both referring to lashes. Even in Mishnayos, they seem to be used interchangeably. For instance, in Makkos 1:2:
מְעִידִין אָנוּ בְאִישׁ פְּלוֹנִי שֶׁחַיָּב לַחֲבֵרוֹ מָאתַיִם זוּז, וְנִמְצְאוּ זוֹמְמִין, לוֹקִין וּמְשַׁלְּמִין, שֶׁלֹּא הַשֵּׁם הַמְבִיאוֹ לִידֵי מַכּוֹת, מְבִיאוֹ לִידֵי תַשְׁלוּמִין, דִּבְרֵי רַבִּי
"We testify about so-and-so, that he owes his friend 2000 zuz," and they were found to be Zomemim – they are lashed (לוקין) and pay, for the name which brings him to lashes (מכות) does not bring him to payment; these are the words of Rebbe.
In general, the term מכות seems to be used more often in Mishnayos than the term מלקות; Sefaria gives 8 hits for מכות, but just one for מלקות; as verbs, לוקין gets 3 hits, while מכין gets none in the context of lashes.
In the Torah itself, the term מכות seems to be exclusively used (Devarim 25:2-3):
וְהָיָה אִם־בִּן הַכּוֹת הָרָשָׁע וְהִפִּילוֹ הַשֹּׁפֵט וְהִכָּהוּ לְפָנָיו כְּדֵי רִשְׁעָתוֹ בְּמִסְפָּר׃ אַרְבָּעִים יַכֶּנּוּ לֹא יֹסִיף פֶּן־יֹסִיף לְהַכֹּתוֹ עַל־אֵלֶּה מַכָּה רַבָּה וְנִקְלָה אָחִיךָ לְעֵינֶיךָ׃
And it will be if the guilty one is flogged [הכות], the judge will lay him down and hit him [והכהו] before him according to his wickedness in number. Forty shall he hit him [יכנו]; he shall not add, lest he continues to hit him [להכתו] on these a great blow [מכה] and your brother is denigrated1 before your eyes.
Is this just a linguistic difference, that the term מלקות began creeping in over the generations, or is there an actual difference between the two terms?
1That's ונקלה, not ונלקה; thus the term מלקות is not used in this passage.