I have seen many different implementations of the same basic CRC-32 algorithm shown below:
int remain;
int sbox[SIZESBOX];
int dividend;
int bit;
for(dividend = 0; dividend < SIZESBOX; dividend++)
{
remain = dividend << 24;
for(bit = 0; bit < 8; bit++)
{
if(remain & TOPBIT)
{
remain = (remain << 1) ^ POLYNOMIAL;
}
else
{
remain = (remain << 1);
}
}
sbox[dividend] = remain;
}
Some of them XOR the dividend before going into the sbox. Others XOR before going into the bit loop, and others use bitwise reflection.
Are there differences that I need to consider between the varying implementations of CRC-32 for a given use case? Is one that uses bitwise reflection or XOR-OUT necessarily better than one that doesn't? Why are there so many different implementations anyway?
CRC32 isn't secure in any way, so from a crypto standpoint the variations aren't relevant. It might affect the distribution properties, but I doubt that's relevant either.
A CRC is just a checksum, protecting against random changed(in particular bitflips) but can't be used as a cryptographic hash. You should use SHA-1 or better for that.
CRC32 is not a cryptographic algorithm, so your question makes me think you need to consider what you're using it for long and hard.