"Relay" is a general term: it's a switch that is opened and/or closed by an electric control signal. These days, relays are available that are of the traditional electromechanical type, or they can be solid state (semiconductor based, employing a transistor, SCR, TRIAC, etc..)
An electromechanical relay is a specific type of relay, where by the electrical control signal goes to an electromagnetic coil which has influence over a moving part of the switch which is made of a ferromagnetic material. In a typical automotive 30-40 amp relay, there is a small coil that pulls on a piece of steel to which the moving part of an SPST or SPDT switch is riveted.
"Solenoid" is a general term for an electromechanical device where you have an electromagnet coil pulling on a ferromagnetic pole piece to convert electrical energy into mechanical energy. Typical design has wire wrapped around a hollow tube, and the moving piece is an iron rod that gets pulled into the tube. There is usually a spring to return the iron piece when current to the coil is removed.
In automotive electrical parlance, "solenoid" can refer to a specific type of high-current electromagnetic relay that makes use of a solenoid to pull the electrical contacts closed (or open). A starter "solenoid" would be more accurately described as a "solenoid type relay". Note that in your car there are also solenoids that control things other than switches, such as the ones that open and close power door locks.
An electrical contactor, such as those used to start AC electric motors, is usually a solenoid type relay with a double-break design (schematically two switches in series to improve resistance to arcing). A "motor starter" is a contactor plus a set of thermal overload protectors which are a sort of resettable really-slow-blow fuse that allows the motor's inrush current while still providing protection against stalls and other faults.
To answer your main question, of whether you can use the starter solenoid as a relay: not necessarily!!! A starter solenoid IS a relay, BUT they are not usually designed for continuous current through the coil. In short, it might burn up if used as you propose. A starter solenoid's coil is only expected to see current for a few seconds at a time--while cranking--so some cost-saving shortcuts are usually made in it's design. It might draw more current for those few seconds than it can handle continously without overheating.
For the application you have outlined, you can use a solenoid relay that looks like a starter solenoid, but it must be one that is specifically rated as having a "continuous duty" coil.
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If you expect your relay to see current in the 80-200 amp range, such as a winch, high-power stereo amp, etc.. you can also use White-Rodgers solenoids that are available with cont. duty coils. McMaster-Carr sells them, and they are also available on ebay and from car customizing places advertised as everything from winch relays to battery isolating contactors. I have seen the White-Rodgers products also rebranded as "Stinger SR80 and SR200", "Lightning Audio", and a few other names I forget.
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I realize this thread is 5 years old but it kinda relates to my question. I'm going to be wiring up a taurus fan in my 77 F100, I've already done the 3g 130 amp alternator upgrade. Ok on to my question, below is the schematic of how I want to wire the fan to work. Problem is Relay #2 isn't big enough alone to power the high side setting. So as I added in the schematic can I wire an 80 continuous duty solenoid to kick on from terminal 87 of Relay #2. That way I can run 8 gauge wire to the solenoid and onto the fan.
I don't know why that came out so small? Sorry if you can't see it good enough I'll try to upload it again to be bigger.
'77 F100 302 C4 John Deere Blitz Black and Cragar Soft 8s
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