I am right now studying a lot of German vocabulary and I often find words that to me have just one translation. In this case I would say they both simply mean: result. I would like to know if there is something that differenciates these words substantially or not. Is one more used than the other? In which way?
There's no difference whatsoever. Can't think of an example where one of which would be wrong.
I looked at the collocations listed by Wortschatz-Portal.
Typical collocations of Ergebnis deal with money (Steuern, Euro, Zinsen, Umsatz, ...).
Collocations of Resultat refer to votes (Abstimmung, Wahl, Stimmen) although you would usually say Wahlergebnis.
Ergebnis is used approximately 5 to 6 times more often (Wortschatz-Portal: Ergebnis 57415 usages, Resultat 9443 usages, see also this Ngram), so it's hard to compare them anyway.
One (Resultat) is of Latin origin, making it a loan word which coexists alongside the German word Ergebnis. You may want to read The Emergence of German as a Literary Language 1700–1775 by Eric A. Blackall, which explains how loan words and Latin influenced German. German was not used in Germany for serious scholarship or legal purposes until the late 18th century. German has many 'pairs' of such words whose meanings are more or less identical and are translated as identical.
English also has such pairs of Latin and Saxon words, too many to list. Often the Latin words are used to achieve a higher 'register', in more formal contexts. Read Lincoln's Gettysburg Address to see how skillfully he uses both kinds of words, depending on the effect he is trying to create. Many of the words are Latinate, as befits the formality of the occasion, but of course not all:
Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.
Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this.
But, in a larger sense, we can not dedicate -- we can not consecrate -- we can not hallow -- this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us -- that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion -- that we here highly resolve that these dead shall not have died in vain -- that this nation, under God, shall have a new birth of freedom -- and that government of the people, by the people, for the people, shall not perish from the earth.