Impeachment is analogous to indictment in regular court proceedings; trial by the other house is analogous to the trial before judge and jury in regular courts. Typically, the lower house of the legislature impeaches the official and the upper house conducts the trial.
At the federal level of government, agencies such as the U.S. Department of Justice's Civil Rights Division, the U.S. Department of Education's Office for Civil Rights, and the Equal Employment Opportunity Commission (EEOC) investigate claims of civil rights violations and discrimination.
A civil case is a private case where someone sues someone else. This is also known as a suit or action. In a criminal case, the Crown prosecutes an accused under a public-law statute such as the Criminal Code or the Controlled Drugs and Substances Act.