Relay Minimum Switching Current
As the other replies say, the 40mA is your nominal coil operate current, and the 10mA is the minimum 'wetting' current that is needed to guarantee the specified closed resistance of the contacts. Different contact materials have different characteristics, generally divided into low voltage and high power. Low voltage ones burn easily, high power ones need a significant current to ensure proper contact.

As you have a limited power budget, here is a trick you can use. You notice the 'must release' specification is 5% of the nominal voltage. It is always the case that once a relay has closed, it needs far less current to hold it closed than it took to close it. Often it will tolerate a drop to 25% of the nominal closing current before it drops out. You would need to experiment to find out what yours will do.

The trick is to drive the relay coil through a parallel RC combination. The capacitor gets the nominal switching voltage to the relay, for long enough to close it. The resistor is sized to continue to conduct just enough current to hold it closed. After operation, the capacitor has to discharge through the resistor, so there is an upper limit to how fast the relay can be switched like this.