If it has emitter and collector, it is not a MOSFET, it's a BJT (a k a "70's transistor.")
BJTs let current through between collector and emitter when there is also a current (the right way) through the base. This means that there will always be current flowing through the base in addition to the switched current when it is on. This make it easy to switch them on and off with a single switch -- current flows, transistor on; current interrupted, transistor off.
MOSFETS let the current through one way ("body diode" direction) always, with some body diode resistance. However, when you charge the gate capacitor (meaning apply a voltage and a short spike of current) they will conduct equally well in both directions. When wired with the controlled voltage against the body diode (normal,) this means they are "off" when the gate voltage is low, and "on" when the gate voltage is high. This actually saves power, because there is no "wasted" current through the gate, other than when switching state.
However, this also makes a MOSFET annoying to switch, because you need to actively pull it UP (charge) when turning on, and DOWN (discharge) when turning off. (This is for N-channel; P-channel is approximately inverse.) Thus, a simple make-or-break switch won't work, unless you replace one of the "pull" directions with a resistor. The output of the Arduino is already switched both ways -- it either ties to VCC, or to ground, so it can drive a gate directly. The output of an optocoupler is not, though, hence this confusion.
For a MOSFET, the allowable voltage from source to gate (what controls the built-in gate capacitor) is different from the allowable voltage from source to drain (the controlled voltage.) A typical low-voltage device might allow 20V from source (0-reference) to gate, and 30 volts from source (0-reference) to drain. (IRLB8721 for example -- popular 30V D/S device with 4.5V recommended gate voltage and 20V max G?S voltage) Here's an example data sheet showing those voltages:
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CDEQFjAA&url=http%3A%2F%2Fwww.adafruit.com%2Fdatasheets%2Firlb8721pbf.pdf&ei=IZiNUKaZM8LtiwKghYHADA&usg=AFQjCNGUrxQ2jGVS0ZaY7Mic2FOCkETjEQ