What is the difference between habeas corpus and bill of attainder in lay terms?

They are very different -- almost the opposite of each other.

A bill of attainder is a legislative act that singles out an individual or group for punishment without a trial.

Habeas corpus (a Latin phrase meaning "you have the body") is a civil proceeding used to review the legality of a prisoner's confinement in criminal cases.

Habeas corpus actions are commonly used as a means of reviewing state or federal criminal convictions. The petitioner alleges the convictions violated state or federal constitutional rights. State habeas proceedings start in state District Court; federal habeas proceedings start in federal District Court. Lower court decisions may be appealed to appellate courts.

Therefore, a bill of attainder adds to the power of the government (i.e., the legislative branch), while habeas corpus is a limit on the power of the government (i.e., the executive branch).