put a fire out和put out a fire区别

--------你问题中的两者完全一样,可互换.
原因是 put out 是 v.+ adv..这类结构中 若宾语是名词,可置于中间 (put the fire out) 或后面 (put out the fire).
再例子：
put your shoes on = put on your shoes
take your hat off = take off your hat
若宾语是代词,则其只有一个位置：中间!
如：There was a fire; we couldn't put it out.
错：There was a fire; we couldn't put out it.(错错错)
再例：
These are your shoes; put them on.
错：These are your shoes; put on them.(错错错)
如果是 v.+ prep.不论宾语是名词还是代词,只有一个位置：后面!
例子：
对：I was looking for my dog when I saw the accident.(宾语是名词,后置)
错：I was looking my dog for when I saw the accident.
对：I've got a pet dog.Can you look after it for me when I'm away?I'll be back in three days.(宾语是代词,也得后置!)
错：I've got a pet dog.Can you look it after for me when...