The recording of genealogical families does provide for the blood, and adoptive relationships. However to join many lineage societies, one must have a "proven" blood line to the historical ancestor, and in some cases a "proven" "legitimate" blood line to the historical ancestor.
I have put the word "proven" in quotes as most of the lineage organizations base the "proof" only on the paper documented line. The DNA science is not really embraced in that realm yet.
The "legitimate" line requires that only those born out of a marriage may be considered. This rules out the adoptive and the out of wedlock children in these societies.
Some societies only require "proof" of the blood line, and could care less about marriage.
For purposes of ones own family interests both the adoptive, and where the information is available, blood lines should be recorded and passed down. This is important for children that were adopted a little later than birth as they usually have been exposed to two family cultures, and in later life may revert to the cultural sense of their blood line over their adoptive.
The other important reason for wanting to know about the blood line is for the history of medical conditions that may be genetic in nature, such as the potential of adult onset diabetes.

I am a research genealogist, and have worked on all of the mentioned situations. Sometimes for legal issues, sometime for medical issues, and sometimes for the personal knowledge of my client.