I’m from Mexico and the way I learned the musical notes was by their sound, however some friends from other places learned the notes with letters.
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Other people have given great explanation, so this is just what I have to add:
The method most Americans use is called the Kodály method, named after Zoltán Kodály (not pronounced how you think). Kodály is who you have to thank for the [hand gestures](https://hungarytoday.hu/wp-content/uploads/2016/05/solfege_ladder.jpg) that go with the Solfège, but there’s a lot more than that.
If you want to describe the 3rd scale degree you’d say “Mi”. But what if we’re in a minor key. We can’t sacrifice the Tonic meaning of “Do”, so what do we say for a flat “Mi”? We say “Me” (pronounces ‘May’). Basically replace the vowel sound to any solfège syllable with the “e” and you get it’s flat form. What about sharp 4? “Fi”. It gets a little irregular though when you think “what’s the sharp third scale degree” or “what’s the flat second scale degree”, but what’s important is that now we have a way of expressing the melodic function of pitches without having to contextualize them by specifying key.
As for the origin of the Solfège syllables, it’s a really cool story. In the Middle Ages, long before we had modern tuning or theory or scales, people thought of scales in the context of the “[hexachord](https://en.m.wikipedia.org/wiki/Hexachord)” (“six notes”). Music theorists back then declared that pitches ought to be grouped in six, leading stepwise up, and the arrangement of these six pitches determined the mode (basically the church modes we know and love: Phrygian, Dorian, Hypodorian, etc).
There used to be no name for any of these pitches. Your choir director just told you “hey, this song’s in Lydian,” and would give you a note, and that’s where you start. But a dude named [Guido of Arezzo](https://en.m.wikipedia.org/wiki/Guido_of_Arezzo) decided it’d be easier for his choir to learn psalms if they had names for each of the notes. So he turned to a psalm called [Ut queant laxis](https://en.m.wikipedia.org/wiki/Ut_queant_laxis), which had a nifty trick where it began a phrase starting on the first pitch, and the next phrase began on the next pitch, then the third, fourth, etc, all the way up the hexachord. He took the first syllable of the first pitch of each phrase, and got:
“Ut, re, mi, fa, sol, la”
Now, back then they used the syllable “ut” instead of “do”. I’m not sure why we changed it, but I’m sure there is a wonderful anecdotal explanation behind it, but my best guess is that all the other syllables begin with a consonant, so they’re more articulated and easier to sing.
This system caught on, especially in the context where it began: the Roman Catholic Church. Because of this, the “fixed-do” method of Solfège being the actual names of notes exists mostly in countries with a catholic tradition, usually speaking *Roman*tic languages. And since it’s based on the hexachord, the seventh scale degree syllable was added later, which is why there’s disagreement between “Ti” and “Si”, and why in German they call B-flat “B,” and B natural “H”.
tl;dr: Kodály method differentiates between Solfège and letter names as well as giving Solfège for accidentals; origin of Solfège and Guido of Arezzo; musicology is cool you should study it.
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