Calvin the Ant refers to two of Calvin's alter egos.
Calvin the Ant as a humanEditCalvin the Ant appeared in a single Sunday strip as an ant-sized version of Calvin with insect-like behavior. He worked as a regular ant for an ant colony, presumably somewhere outside of his house.
This alter ego was analogous to Calvin's reluctance to pick up his room at his mother's demand.
Calvin the Ant as an antEditCalvin the Ant appeared as an actual (albeit anthropomorphic in behavior) ant in another Sunday strip. There, "sick of working all the time", he took a break from servitude and labor and lay down for others to do the work.
This alter ego was once again analogous to Calvin's reluctance to work around the house.