"Minor" and "Harmonic Minor"
are NOT the same!
this question is vague.
It's like asking if a Ford automobile is the same as a Ford car? Every car is an automobile... but not every automobile is a car. Trucks and buses are also automobiles. Just different kinds. And it makes no difference at all who makes them. (Well... at least not as far as their definitions are concerned.)
Similarly, scales (and chords, which are simultaneously-played subsets of scales) are just collections of intervals. In other words, they're just collections of -spaces- in between notes, relative to a given reference (aka 'tonic' for scales, 'root' for chords). If the collection of notes are spaced the same (relative to the reference note), then the scale and/or chord is the same kind... no matter what key they're in (The notes in chords may be in different orders. These are called inversions, and they can sound slightly different. But their names and definitions are the same (as long as all the notes, have basically the same relationship with the tonic/root/reference).
Now when someone refers to a scale just as a "minor" scale, it's assumed they mean the "Natural Minor" scale. (Because it's the 6th mode of the diatonic major scale, but no need to get into that now.) In addition to the mandatory flatted (or "minor") 3rd, it also has its 6th and 7th degrees flatted by a half-step as well.
But whether it is minor or major is only based on whether there's a note a step-and-a half up from the root, or if there is one, two whole steps up from the root, respectively. If the scale (or chord) has neither (or both) it is ambiguously-hard to say whether it's major of minor, although the nature can be suggested (and/or indirectly stated) by the kinds of 6ths and 7ths which may be present. (The 2nd, 4th and 5th generally serve other functions.)
As for the 'Harmonic' part:
Standard 'diatonic' scales are collections of notes with either "tones" (aka "whole-steps") or "semitones" (aka half steps") in-between them. All 7 modes of major scale are this way. (And the fact of these two types of standard-sized building-block intervals, is why such music is called "diatonic".) But some scales break this... guideline-like rule. For some scales have larger intervals between some of their member notes (aka degrees). With too many big ones, then fewer notes (than the standard 7) can fit in the scale. And when there are lots of small ones (like the chromatic scale) they can contain more.
But when one simply refers to just "the harmonic minor scale" (as this question did), of the many possibilities, it's generally understood to mean the slight modification to the pattern of intervals of the natural minor scale (aka Aeolian mode of the Major scale), where the normally-flatted 7th is left major. In other words, 1,2,♭3,4,5,♭6,7 instead of the 1,2,♭3,4,5,♭6,♭7 of the natural minor. (Or instead of the A,B,C,D,E,F,G of A minor, the A Harmonic Minor scale is A,B,C,D,E,F,G♯)
The normal flatted 6th, next to the unusual (for minor) major 7th, creates an unusually large 1 1/2 semitone interval (in the second half of the scale, aka 2nd tetrachord). And that's why it's called harmonic. Not necessarily "harmonic minor" mind-you! Just harmonic. For once again, if the 3rd is major... then it'll be a called (some sort of) harmonic major scale. And there are scales that also have a larger-than-normal interval in the 1st half of the scale (ie: in both tetrachords), which are therefore called "Double-Harmonic" scales... again, either major or minor, depending exclusively on the type of third they have.