Are there any significant differences between two Apple products of the same name but different part numbers (particularly FC371LL/A and MC371LL/A)?

I was going to buy a refurbished MacBook Pro 15" but when I compared it to a regular one added in the shopping cart for reference, I found that they had different part numbers: FC371LL/A and MC371LL/A. I was not sure if the old model had something wrong, so I haven't ordered. Does anyone know any particular fixes Apple has done to the new MacBook Pro line?

Also, are Apple products of the same name but different part numbers significantly varied?

The refurbished one probably has a different part number because it is refurbished now new.

It won't have anything "wrong" with it, but it is refurbished. Check the specs and compare it to the current production model. Typically they will say "late 2010 model" or something of the sort to indicate if this is different (hardware wise) from the current one.