When I search for differences between harmony and counterpoint I usually read that in the end there's harmony in counterpoint. Can't I learn just harmony and get the same results ?
Well, counterpoint is not harmonization. The main difference is that counterpoint has its own melodic and rhythmic identity. If you take a look at, say, Bach's great choral works, you'll find some pieces labelled "Choral" which are mainly a melody with harmonization, and some pieces labelled "Chorus" which are strongly oriented along lines of counterpoint with individual lines and rhythms. While Bach is pretty good even in making harmonizations make sense of their own, the difference in character and complexity is pretty striking.
Here is a link with some simple counterpoint analysis of Counterpoint 1 in the Art of Fugue. I'm not going into detail here, but while the link is available, it is nice to look at the unfolding of structure it provides.
A more elaborate study for counterpoint is the Credo in Bach's B Minor Mass. The first part is in an "ars antiqua" style of "classical counterpoint" (obviously, not "classical" as the music period since that comes after Bach). The second part (Credo, patrem omnipotentem...) after an intermission is in a Bach-typical style that is more intricate but also more "operatic" regarding the changes of character and polyphony within the piece.
You'll find that "harmony" is far from being the topmost apparent category in the composition even though it's there as a sort-of emergent phenomenon between the independent voices (of course, this sort of emerging is not accidental but rather the result of hard work and design, but it is not the main "feature" but "merely" support structure).
Counterpoint is the study of how to make voices (musical lines) independent. It is not simply just harmony. Harmony comes into play, but if you are working on anything tonal harmony will come into play.
The common examples of counterpoint is Bach and Fux, but can be seen a lot in modern music. The most common places you would see counterpoint today is in background vocals and anything where there is more then melody at a time.
If you want to write anything where two or more musical lines work together, but sound independent then learning counterpoint is a must.
No; each are separate. Harmony is vertical and treats tones as singular, sonorous entities. Counterpoint is horizontal, and indicates direction. There is harmony in counterpoint, however, it is treated as incidental with the priority being the emphasis of musical line and direction.
Each is separate but equal. You could be a master of voice-leading but craft very weak musical lines. Conversely, you could create compelling musical lines but have a very poorly conceived harmonic progression.
For the purposes of scope I'm confining my comments to 17th-18th century counterpoint and harmony. Other types of counterpoint, such as modal, atonal, and serial follow very different ideologies.
TL;DR: when you "learn harmony" it's about a different style of music than when you "learn counterpoint."
Nearly everyone agrees that harmony and counterpoint are related, and that you can't avoid learning about one when you learn about the other. But what you're really asking about is harmony and counterpoint as topics of study. Harmony courses (textbooks, tutorials, etc.) and counterpoint courses teach both harmony and counterpoint as elements of music, but about different musical styles.
Harmony courses tend to be about Common Practice Period style, a synthesized abstraction used to model the harmonic and contrapuntal relationships prevalent in some Western music from about 1750 to 1900. Counterpoint courses tend to be about another synthesized style used to model the harmonic and contrapuntal relationships prevalent in some Western music from about 1600 to 1750. When you take a course in one of these topics, you're learning a historically informed, but not historically accurate, strategy for composing and analyzing music from those different time periods. Whether this is something you need or want depends on your educational goals!
(NB: my opinion is that harmony courses teach an abstraction of Beethoven's piano sonatas, and counterpoint courses teach an abstraction of Bach's keyboard fugues. Proving either of those would take a doctoral thesis!)
Harmony can be as simple as one melody with an accompaniment.
Counterpoint is a conversation between equal voices. There is an exchange occurring between the voices.
The very best counterpoint does in fact combine both, because the voices when played together generate a chord progression (as I found out when examining the opening of the last art of fugue piece, the unfinished one). But nevertheless, this IMPLIED harmony is not explicit.. what the naive listener hears is a couple of voices simply having a conversation.
The entire fun of counterpoint is to hear all the melodies by themselves, and to hear the joint effect as they play in combination. Its like trying to listen to several people talking on top of each other. It is difficult, but very rewarding.
Harmonic music is much simpler; one voice, with a backing group in the background.