Matched and Identical Concepts of Transistors
Identical transistors are very easy to find....... in your SPICE simulator. This can sometimes be misleading, when your circuit has superb performance, because everything matches perfectly, distortions cancel, etc.

If you pick two transistors from the bag, they will have different characteristics (Vbe, hFe, capacitances, Vgs, RdsON, etc).

Also, your transistors will be at different temperatures. Vbe changes 2mV/°C for bipolars, hFe changes too, and FETs are also temperature-dependent.

This will create offset, distortion, and drift in your current mirror.

If you want a better current mirror (or differential pair), you can:


Add degeneration resistors, to swamp differences in Vbe.
Use matched transistors, like DMMT3904 which have matching guarantees, and they are in the same package, ensuring close (but not identical) temperature, at least if dissipation isn't too imbalanced. These are two independent transistor chips, so they are isolated.
Use dual monolithic transistors, which are made on the same chip, therefore much better matched, also better temperature tracking, and very expensive.
Or, in an IC, you can have excellent matching, because transistors are made next to each other on the wafer, in the same fab run, same process, etc, so they will have very close characteristics.