An Immigrant is a person who has citizenship in one country but who enters a different country to set up a permanent residence. Just entering another country does not make you an immigrant. In order to be an immigrant you must have citizenship in one country, and you must have gone to a different country with the specific intention of living there.
There is a further classification, whether or not you are a legal immigrant. A legal immigrant is a person who has entered a country different from the country where they have citizenship with the purpose of setting up a permanent residence in the new country while first receiving the proper visa and clearance to enter the new country and settle. An illegal or undocumented immigrant is a person who enters a country different from the country where they have citizenship with the intention to set up a permanent residence but without receiving the proper clearance.
Just visiting another country does not make you an immigrant. Entering another country for a temporary stay, whether for work, study, or other reasons, gives you non-immigrant status, and you will have to obtain a different kind of clearance.
As a legal immigrant you will not be required to show proof that you have an intention of returning to the country of your current citizenship. You will have to obtain an immigrant visa or some other document that certifies that you are elligible to enter the country you wish to immigrate into.
You can gain an immigrant status in many different ways, according to the laws of the country you wish to immigrate to. In many cases the family members of citizens may be allowed to immigrate to the country and gain citizenship. Also, if there is a demonstrated lack of qualified naturals for a certain employment position, then you may be allowed to gain an immigrant status if you are qualified for that position. It is also possible to gain an immigrant status by seeking refuge (from outside the country), or asylum (from inside the country) if you can prove that you are in a specific danger if you return to the country of your citizenship.