Sometimes, I come across with strange 'ordinary' verbs which has two forms and they are not phrasal verbs:
You have to bandage that cut. You have to bandage up that cut.
Chop the onions roughly. Chop up the onions roughly.
I was very stressed before the exam. I was very stressed out before the exam.
Why there are so many forms?!
Which one should I use and when should I use particular form?
Is there because of AmE and BrE or other things?
These are examples of what are called Phrasal Verbs.
A phrasal verb consists of two parts:
Phrasal verbs usually mean something different from the usual use of the verb; occasionally they are predictable, but most of them have to be learned individually. As @medica says, they are idiomatic. However, they do have structure, and, since most English verbs form one or more phrasal verbs, frequently several, phrasal verbs actually constitute the majority of English verbs, so they are worth learning about.
For instance, the phrasal verbs formed from the verbs and particles mentioned above — each an English verb with its own individual sense — include:
A good dictionary will include idiomatic phrasal verbs.
There are also dictionaries of phrasal verbs, which are quite fascinating to study.
These are examples of idiomatic language. There is no rule guiding idiomatic use; people use it because they've heard it in their region, their home, their peer group. How it starts, I can only guess. Somewhere along the line, someone thought the extra word helped the verb to express more clearly what they wanted to express.
Use of idiomatic language can also indicate belonging. The classes can be: educated, race, area, ethnicity, beliefs, etc.
Chop the onions is a complete sentence. Up is an unnecessary addition. It does not impart a different meaning.
I was very stressed... Again, complete. Stressed out is popular among the young and is a kind of idiomatic expression. It may indicate to some an emphatic element. But in my experience, it's likely that the person saying stressed out is either young or spends a lot of time in the company of the young.
This is a good question for linguistic anthropologists - those who study the role of languages in the social lives of individuals and communities.
Because English gets around. The simple verb on it's own is normal in English but when the language was exported to other countries some speakers adopted grammar from their own language into English. So in parts of the US where the inhabitants had spoken Spanish or French they kept their own grammar when speaking English.
There are some cases where formal English has an extra form, generally this is because of efforts in the 17/18 century to copy Latin or French to add elegance and sophistication to the language.
As others have mentioned, the use of so-called phrasal verbs can be subject to highly idiomatic and essentially unpredictable or unsystematic usage.
In the particular cases you mention, it is fairly common for the phrasal version to emphasise the notion of completion. So if you "bandage up" a wound, as opposed to simply "bandaging" it, this emphasises the idea that the wound is completely covered by the bandage. The preposition up is used to indicate "complete removal" in a number of cases (cf. "eat up", "drink up", "soak up"...). In some other cases, it emphasises the "result" rather than the "process" (e.g. "make" vs "make up"; "add" vs "add up").
Which specific preposition is used to make the phrasal verb is quite a complex issue. Different prepositions tend to suggest different metaphors and very often there's a choice. For example, "clean up"/"clean out", "hoover up/hoover out" essentially mean "remove the dirt from", but of the two, "up" suggests extraction from a surface, whereas "out" suggests extraction that leaves the surfaces of a closed space visible ("hoover up the mess", "lick up the sauce [off your plate]" vs "hoover out the cage", "lick out the bowl").
You can beat someone.
You can beat up someone.
You can beat up on someone.
Who can explain it? Just try to keep pace with changing fashion.
