When collectors wish to acquire a particular category of chip or token, it helps to have a name for it. I collect counterfeit chips, and my collection is very small! Those who, in addition, collect fantasies and copies will have very very large collections.

Regarding the "illegal" classification, I much prefer "unlicensed" as a way of distinguishing these from casinos and cardrooms that had a license from the state to operate. Some places (Oregon for example) had unlicensed cardrooms with chips that were NOT illegal as the state chose not to get involved with regulating them at the time. Social gaming it is sometimes called.

Not sure what you mean by "underground" as I've not heard this term used as a chip classification. The term "underground club" is sometimes used for operations that choose to operate on the sly without advertising and without attempting to get the sanction of the government.