What is difference between mosfet trigger switch module and half bridge motor driver module
to this
A MOSFET switch allows to turn the motor in one direction. A single half H-bridge cannot do more, but a full H-bridge (2 half H-bridges) allow to turn a motor in both directions.
Can you explain further?
The switch is a single MOSFET switch (two MOSFETs are paralleled for more current handling, its a single switch though).
The second picture seems to be a dual H-bridge (L298), which isn't MOSFET based and much more limited in current handling (and pretty obsolete as a result).
A half-H-bridge is two MOSFETs in a totem-pole configuration. Its half of an H-bridge as the name suggests. Two of them make an H-bridge for bi-directional DC motor control, three of them can drive a 3-phase motor (BLDC, AC servo, induction, etc).
Wikipedia and/or electronics stack-exchange probably has articles on such things.
What do you want to do?
Hard to say.
OP appears to be MIA! 
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