This may be too general of a question, Relay question

Relays vary some on the design. The fast closing ones usual require more operating power. Designing a relay is very involved.
You have to take into account the spring tension, closing time, and temperature rise of the inner most winding of the coil when ran continuously.
 
How much amps and or volts does the signal/trigger side of a relay normally draw?
More so a 12v 40 amp max relay.
Pick a specific relay from a major relay manufacturer, then consult their datasheet. This is a critical spec so any reputable manufacturer will provide it.

Your question was kind of vague, so my answer is too. In other words, it's a resistive/inductive coil with (hopefully, since it isn't overheating if the right part for the application) negligible change in resistance, so say a relay spec'd as nominal 12V to draw 100mA at 12V. If only given 9V, it will probably trigger still, and will draw less than 100mA doing so, but be less reliable in triggering (in extreme operating conditions) since the target operation was 12V, but the datasheet may still quantify that as a reliable operating voltage. If given 14V, it will draw more than 100mA. Here is where charts and graphs on a datasheet come in, or your own testing.
 
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