Question
QUESTION: our firewood has mushroom looking fungus growing on it ... is it safe just to knock it off and then burn it?

ANSWER: These are the fruiting bodies of a decay fungi. The wood is decaying. It will not harm anything to burn the wood. Since it is decaying it may not burn as hot or long as solid wood but I would go ahead and use it first to get rid of it.

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QUESTION: what is the diff. in 'decaying wood' and 'solid wood' because this wood was freshly cut down this spring ... and the fungi grew on it during the summer ... does some wood decay faster than others?
thanks.

Answer
Solid wood is hard and usually not discolored. Where decaying wood is stained and starts to become soft and /or mushy. Fungi will infect wood as soon as it is exposed (wound on a tree, cut logs etc.). Fungi need four things to grow--food (wood), moisture and warmth and Oxygen.   More than likely  what you have is fungi decaying the bark and just beginning to enter the wood. Yes some species will decay faster than others--pine and the conifers decay usually the fastest where hickory and oak ere slower to decay. Here in the Deep South firewood if left where moisture can get to it will decay fairly fast say maybe the third year some of it is very light and breaks apart.  

IF the center of the logs are stained and softer then the outer wood I would guess that the tree had some decay started before you cut it--more than likely from a wound.

In any case wood this wood is still good and do not worry about the fungi mushrooms they will burn in the fire and not be a problem.