the virtual short
When negative feedback is present, the op-amp forces its two inputs to the same voltage, as if a wire shorted them together, except there is no wire and no current flows between them. This is the general statement; the virtual ground is just the special case where the plus input happens to be at 0 V.
The two golden rules describe it exactly. Rule 2 says V+ equals V-, so whatever voltage you put on one input appears on the other. Rule 1 says no current flows into either input, so the two are not actually connected. The node is therefore a short for voltage but an open for current: the inputs track each other in voltage while staying perfectly isolated. If you set the plus input to 2 V, the minus input also becomes 2 V, without any current passing between them.
This lets you read off the voltage at the minus node instantly: it equals whatever the plus input is being held at. That shortcut is how the non-inverting amplifier's gain is derived. The honest reminder is in the word virtual: a meter really does measure equal voltages on the two pins, but they are not physically connected, and that equality vanishes the moment feedback is removed or the output saturates.
Non-inverting amp: set the plus input to 2 V, so by the virtual short the minus input is also 2 V. With a 10 kilohm feedback resistor and a 10 kilohm resistor to ground, the output must swing to 4 V, because that divider puts 2 V back at the minus node.
Equal input voltages plus zero input current makes the algebra fall out in one line.
It is virtual: the two pins really sit at equal voltages, but they are not physically connected, and the equality disappears without feedback.