IIRC, a standard rate turn is 3 degrees per second and turn you 180 degrees
in 1 minute.

Yes. (At least for piston powered planes. Jets may use half that IIRC)

So [...] what's a constant rate one?

Any turn at a constant rate of angular change. A standard rate turn is
an example of a constant rate turn. A half standard rate turn is another.

the turn indicator is a gyro instrument
just like the attitude indicator which also
indicates bank.

It is a gyro instrument, yes, but it isn't "just like the attitude
indicator". Don't let the display confuse you. The gyro is set at an
angle, and when the airplane turns, a force develops between the
airplane and the fixed axis of the gyro. This turns an indicator. The
gyro =will= be dragged unwillingly around the turn, complaining the
whole while. (This "complaint" is the turn indication

By choosing the angle carefully, one can also have the =rate= of change
of bank be incorporated into the indication, providing a more rapid
response, at the expense of purity of indication.

And for your last question, yes, for that reason the standard rate turn
will indicate the same no matter what the speed and bank angle, because
the gyro is not responding to bank angle. It is responding to the
rapidity of change of nose direction.

Jose
--
Get high on gasoline: fly an airplane.
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