Bocs is very informal, typically used among friends. If you did something very bad that needs a more serious apology, you should stick to 'Bocsánat', even if among friends (otherwise, 'bocs' would sound like a half-assed sorry). If you want to be cute (again, in an informal setting) you can say 'bocsi' or 'bocsika' for extra cuteness <3
Sometimes it is not too easy to hear the difference in a casual situation. It also depends on the region, average age and age distribution in the local subculture. "Bocs" is not rare but it is possible that in a university, a neighborhood or a region has the preference for "bocsi". But that is even more colloquial than "bocs" and it is better to avoid in formal ocassions.
"aplogies" is a typo ;) Of course it is apologies. "bocsánatot kérek" is the most formal, it is often used to show respect, too.
Slang and chat lingo uses many forms usually based on "bocs" and starting with it. If a word starts with "bocs" you can suppose that it is a variant of "bocsánat" (Examples are "bocsi", "bocsesz", "bocsika" are very common, and the list is very far from complete. You can often hear them on the streets, etc.)
jani678913: check out the levels. If it is below 10 that is usually just a curiosity not real learning. Serious study often involves 20+ levels. In my case Italian is the language I really learn, and I am somewhat fluent in English and I practice now and then. All other languages are short acquintances driven by curiosity only. :)
I think this is a bit late reply, but you're completely right! Hungarian is in secondary relation with some turkic languages (but the level of relation is wildly debated) and we have tons of borrowed and adopted words. Anya, apa, alma, zseb, etc. Just go to Google Translate and try to put this to Turkish: "zsebemben sok kicsi alma van" Then try to say them in both languages—they are almost exactly the same :D
We also have many words borrowed from Slavic languages. Hungarians lived more than a thousand of years among Slavic people, and there are many influences. Medve is one of them, it is direct descendent of medved, but there are lot more. And, as the common official language was German during the XVII to XIX centuries, we also have many borrowed words from German, too.
Meanwhile the Hungarian "szablya" made worldwide success and originated even the English "saber"; "kocsi" is the forefather of "coach", "coche", etc. and to my surprise Slovakian word for harp is "harfa" that is clearly comes from Hungarian "hárfa".
"harfa" just happens to be a cognate with everything, it most likely made it's way to Hungarian via German "Harfe" - and since pretty much all other Slavic languages have either "harfa" or "arfa", there is no reason to think this is a mass influence from Hungarian. (The funny coincidence that "fa" is meaningful in Hungarian and "hár" sounds like something that could be meaningful almost got me as well, a couple of months ago. :D)
It actually comes from old Turkish.. http://www.szokincshalo.hu/szotar/?qbetu=b&qsearch=&qdetail=1087
I really don't understand the down votes. Actually many Hungarians agree that our language is one of the weirdest ones—and we're proud of it :D
Also Hungarian is very flexible, and when you master it (after some decades for a non-native speakers) it gives tons of fun and a lot of joy when you can exploit its expressive power and abilities. This flexibility and expressive power makes Hungarian literature sound so strange and diminished in translation. None of my favourite poets and writers translate well (and I do translations quite often, too).
Hungarian is definitely a mouthful, with some interesting constructions arising over two millenia and the evolution of the language. As for poetry, I recall having to memorize and recite Petofi Sandor's "Nemzeti Dal" as a child (sorry - can't type accented characters on this keyboard). Powerful poem of the 1848 revolution in Hungarian, but just doesn't carry into English well.
"Pardon!" ;) It is the easiest to learn and it fits for your need when you're in doubt in a situation like this. We use it sometimes, not too often but it won't be strange. For other words, all of them suit for different circumstances. "Bocsánat" (actually "bocsánatot kérek") is generally used, a bit formal, but not overly. "Elnézést" (or "Elnézést kérek") is frequent, but more formal, while "bocs" is very informal.
You may want to know that "Elnézést [kérek]" means different thing actually, even though I use it for apologize. This literally means "[please] look away" as if the case wouldn't be happened if you won't see... The root of the expression means many things (like "indulge", "look away", "watch something for a long time", "miss" [a target for example], "don't pay attention" [in certain situations only], "look into the distance"). These meanings show that "Elnézést kérek" means actually a request of not noting what happened.
Bocsánat = like "I apologize", it is more formal
Elnézést=a bit less formal, but keeping a distance
Bocs ("bocsi" and many versions) = very colloquial, use only with closest friends and relatives.