Two parallel metal plates have capacitance that depends on their surface area and separation. Parallel wires, while perhaps not as capacitive as plates, also have capacitance that depends on their length and separation. The reactance this causes is inversely proportional to frequency, so the capacitance has no significance at DC and is very significant at radio frequencies.
The calculator computes the capacitance per centimeter of wire length for various wire gauges. It assumes that the two wires are identical, perfectly straight, and parallel to each other. Wire separation is measured from center-to-center, so when it is less than or equal to the wire diameter then the wires are in physical contact. Under these circumstances the calculator shows a result of "infinity."
1Harry E. Green, A Simplified Derivation of the Capacitance of a Two-Wire Transmission Line, IEEE Transactions on Microwave Theory and Techniques, Vol. 47, No. 3, March 1999, p. 365-366.