I presume that you mean that the US State commonly referred to as "Rhode Island" does not appear to be geographically identical to a particular island.

The full and proper name of the state in question is "the State of Rhode Island and Providence Plantations". This state does include a large island named "Rhode Island" (also called Aquidneck Island), a city on the North American mainland named "Providence", and some of the surrounding regions.

Sources:

http://dot.ri.gov/about/maproom/ http://webserver.rilin.state.ri.us/RiConstitution/ConstFull.html

The official name of the state is "The State of Rhode Island and Providence Plantations".

The colony of Rhode Island, was on what is now called "Aquidneck Island", including the towns of Newport and Portsmouth.

The colony of "Providence Plantations" was on the mainland, centered around the town of Providence.

By a royal charter in 1663, from King Charles II, these colonies were merged and granted an elected governor and legislature.

So, the "Rhode Island" part of "Rhode Island and Providence Plantations" is an island. The term, "Rhode Island", however, is usually used to refer to the whole State, not just the island part, as the official name is a long one, and people abbreviate it.