The following is the extract from Wikipedia: ( https://en.wikipedia.org/wiki/Current_conveyor )

The ideal CCII can be seen as an ideal transistor, with perfected characteristics. No current flows into the gate or base which is represented by Y. There is no base-emitter or gate-source voltage drop, so the emitter or source voltage (at X) follows the voltage at Y. The gate or base has an infinite input impedance (Y), while the emitter or source has a zero input impedance (X). Any current out of the emitter or source (X) is reflected at the collector or drain (Z) as a current in, but with an infinite output impedance. Because of this reversal of sense between X and Z currents, this ideal bipolar or field-effect transistor represents a CCII−. If current flowing out of X resulted in the same high-impedance current flowing out of Z, it would be a CCII+

is an ordinary transistor simple nonideal CCII- ?

CCII- may be viewed as an ideal MOS transistor:  Y=gate, X=source, Z=drain

If transistor is nonideal CCII, we need to compare the ideal parameters with that of actual transistor parameters. Actual current flows and impedance need to be considered. 

Thanks for the reply.

CCII + is also called a diamond transistor. And what about CCII. - "inverse, complementary" diamond transistor?

I believe that well-known circuits with transistors could "generate" structures with CCII.