You pose your question about legal and illegal immigrants under the heading of "Economics." Thus I must infer that you mean to ask what is the difference between legal and illegal immigration in relation to economic impact. Two economic points come readily to mind. The first is that, generally speaking, legal immigrants are granted visas on condition of having employment prearranged in a field where there is not intense competition for jobs. In other words, generally speaking, new talent or skill is needed in an industry in this country. In contrast, illegal immigrants generally search, after getting into the country, for menial work that is attained without the sanction of legal identification. The second point is that legal immigrants pay income taxes to the U.S. government while illegal immigrants, who are paid "off the books" without accounting entries in company ledgers, pay no income taxes to the government.
Legal immigrants are those that have moved in from other countries while following the rules and regulations laid down for doing so. From an economic outlook, foreigners are allowed into a country when they are perceived to be an asset. This could be in the form of their skill set and the ability to perform tasks for which there are not sufficient number of people in the country already.
Illegal immigration takes place when foreigners sneak into a country and take up tasks for which there are already a large number of qualified people in the country and many of them are willing to take up the tasks. Illegal immigrants deprive citizens of the nation from employment that they can claim a right to. This is the main reason why immigrants that come in through legal channels benefit a nation while illegal immigrants are a drain on its resources.
Well, the simple answer is that legal immigrants apply to enter the country, follow all the appropriate and required steps, receive official approval, and receive official documentation. Many of them eventually become citizens. I know many people who have gone through the long and arduous process of becoming legal American citizens, and I can't think of one who hasn't made the country stronger and better. I wish we had more such immigrants, and I always think of these people when I read of others who have broken the law by entering the country illegally.
Very simply, Legal Immigrants apply for and receive a visa to become permanent citizens, and Illegal Aliens either do not apply or fail to keep their visa current. Illegal Aliens live in a country without having passed through the proper legal channels to receive citizenship, while Legal Immigrants apply for a visa, present their identification for background checks, pay their entry fees and taxes, and perform all the legal qualifications necessary to become a citizen.
Most other differences vary based on personal opinion, anecdotal evidence, bias, and/or stereotype. As #5 points out, many Illegal Aliens in the U.S. are successful and educated; a Legal or Illegal Alien does not need to conform to any definition besides the legal.
Apart from the point of view of law, there are other social realities between illegal immigration and legal immigration. With illegal immigration there is the connotation of povery and lack of education or specific skill sets. For this reason those who are characterized a illegal immigrants are not treated as well. Of course, this is not the case. There are many people here is the United States that are illegal immigrants, but they are highly successful and educated.
Good explanations, but is it not also possible for legal immigrants to become illegal immigrants. If someone is here on a student visa, and he stops attending college would he not eventually become an illegal immigrant? Also, it's interesting to me that an illegal immigrant can give birth to a child in the United States, and then that child is considered a U.S. citizen.
In this country, another difference is that one is seen as a good thing and the other is (nowadays, at least) seen as a bad thing. Of course, this has not always been true.
Today, we see illegal immigration as a major problem. People who argue for a serious crackdown on it tend to take care to emphasize that they love legal immigrants but hate illegal immigration. So, in addition to the legal/technical difference stated above, there is also a difference (nowadays at least) in public perceptions.
These are all very different questions and should probably be posted separately so they can be answered more fully. I will address the last question.
Legal immigration is where a citizen of another country comes into this one through legal channels. These legal channels often start with a visa or passport. A student might come on a student visa or a worker might come on a work visa. If they wanted to stay, they would apply for citizenship before their visa or passport expired. There is a lengthy process for gaining citizenship, but it can be accomplished. For a time, a spouse was granted automatic citizenship, but this is no longer the case. A legal immigrant is someone who is granted a green card under a particular set of circumstances.
An illegal immigrant is a person who has entered another country illegally. They might have crossed the boarder without a going through check points and without documentation. They might be someone who has entered the country under a visa or passport and stayed beyond the expiration of this pass. Illegal immigrants do not have the legal right or the proper documentation to be in the country.