More than likely the same family, but the common link is probably several generations back.

The spelling variation, I have heard is due to the fact that some folks wanted to distance themselves from other family members, so they would ad an S or D or subtract an S or D.

A good resource for the Davisson family line is:

http://contentdm.lib.byu.edu/cdm4/document.php?CISOROOT=/FH9...

Go to the bottom, expand the printing version and download the both parts.

Let me know what you think.