How to interpret voltage/current for relay?
The switch contacts are rated 10A at 250 VAC, 10A at 120 VAC.  There appear to be two specs for 28 VDC, 15A and 12A.  It's not clear which one applies to what cases just from the markings on the relay.  Look up the part number to find the datasheet.  That should tell you for sure.

The "12VDC" in the part number is almost certainly a indication that the coil is intended to be run from 12 VDC.  But again, look at the datasheet for the real info.  You can't expect all possible specs to be printed on the case.

Added now that datasheet is available

It is very common for relay manufacturers to design the mechanism once, then offer a family of parts with different coil characteristics.  Different customers want different coil voltages, so they make a variety.  The same space can hold lots of turns of a thin wire or fewer turns of a thick wire.  The current required to activate the relay is inversely proportional to the number of turns (cause the same magnetic field).  Longer thinner wire has more resistance, so requires more voltage to operate the relay but at less current.  Typically the power required to activate the relay is roughly the same accross such a family.

The coil data chart shows exactly this for two sub-families, which they call the TRU High Sensitivity and TRU Standard.  The high sensitivity probably has a slightly different mechanical structure so that less magnetism is require to operate the relay.  That may trade off with other specs, like vibration resistance and possibly operating speed.

Each line of that chart therefore refers to a different specific model of the TRU relay product line.  Since your relay is of the high sensitivity variant, the row for 12V in the top section applies.  From that it can be seen that the nominal coil current will be 30 mA, the coil resistance 400 &Omega;, the coil power to operate the relay is 360 mW, the contacts will close at 75% of the rated coil voltage (9.0 V), once engaged at least a 5% drop in coil voltage is required to release, and you shouldn't apply more than 130% (15.6 V) to the coil.

The operation time of 15 ms means that's how long it takes worst case for the contacts to close after you have applied the specified coil voltage.  You can apply this coil voltage and keep the contacts closed indefinitely.  The release time of 5 ms is how long it takes worst case for the contacts to open after the coil is switched off.