U.S. immigration laws contain numerous grounds upon which non-citizens may either be deported back to their country of origin (the technical term for which is "removed") or refused entry into the United States. In fact, the laws divide these grounds into two separate categories:
The grounds of inadmissibility, found in Section 212(a) of the Immigration and Nationality Act (I.N.A.). These apply to a person seeking admission to the United States, including both literally seeking entry at the border and also seeking the right to stay legally, such as with a green card application (lawful permanent residence). In some cases, they can even be applied to green card holders returning to the U.S. after foreign travel.
The grounds of deportability, found in Section 237 of the I.N.A. These apply to a person already legally living within the United States, perhaps with a nonimmigrant (temporary) visa or a green card. They also specify that people who are in the U.S. without legal permission (also referred to as "undocumented" or "illegal") shall be deported.
If the immigration authorities believe that you are deportable, or were inadmissible during your last U.S. entry, removal proceedings may be started against you. You will have a chance to argue your case and in some cases to ask for a waiver (legal forgiveness). However, this might occur in the context of deportation and removal proceedings in immigration court.
In any case, you'll need a lawyer's help with this type of issue.
Once an immigrant becomes a U.S. citizen, that person cannot be removed unless he or she used fraud to gain citizenship or an earlier immigration benefit.
To learn about the waivers and other methods for defending yourself from removal, see Removal (Deportation): Process & Laws.
Here's a brief summary of the types of personal characteristics or history that can make someone inadmissible.
Again, this is just a brief summary, intended to highlight potential trouble areas. Do not attempt to analyze your personal immigration situation based on this list.
For more on being "inadmissible," see Who Can't Get Into The United States?
Here's a brief summary of the types of personal characteristics or history that can make someone deportable.
To read more about the grounds of deportability, see Can I Lose My Green Card and Be Deported?
In short, while there are clear distinctions between the grounds of inadmissibility and the grounds of deportability, both can present problems for non-citizens in the United States. Consult an experienced immigration attorney with any questions or for a personal analysis.