Are lawsuits different from criminal cases and arbitration?
Yes. Lawsuits are civil proceedings, as distinguished from criminal proceedings.
In criminal proceedings the State or Federal Government is seeking, on behalf of the people generally, to punish a person who engaged in conduct made illegal by a criminal statute. If the person accused of the crime or offense is found "guilty", s/he would be subject to possible fine or imprisonment.
Lawsuits are also different from methods of "alternate dispute resolution" such as "Arbitration" (in which a private arbitrator makes the decision), or "mediation" which is a type of structured meeting with the parties and an independent individual who helps the parties fashion an agreement among themselves.