You are correct in thinking "Baird" and "Beard" may be the same family. I understand that the name was pronounced "Beard" back in Scotland and Wales, perhaps leading to that spelling in the US. One can find brothers from the same family using the two different spellings. It must be remembered, also, that many of these people were illiterate, especially as they moved into the frontier where no schools existed.
I see an old post from you asking someone's ties to the family. If that was aimed at me, I come down from P William Baird 1784, youngest son of Dr Ezekial Baird. P Wm moved to the Hickman Co area of Tennessee after 1811. His descendants remained in that area. As I read posts on this thread I see some misinformation about P Wm's children and his brother Blodgett's children. Dr Ezekial kept a family Bible which records the names and birthdates of his earlier grandchildren. Leonard McCown has posted that info from the Bible onto his own website and passed it along to the State of Tennessee. (If you want the most accurate and thoroughly researched information on our Baird line, go to McCown's site. He, too, descends from P William Baird.)
Someone has This Blodgett's first son as "John". Not true. Blodgett's first two sons are Alford (notice spelling) and George Washington. Also, some of P Wm's sons appear to be assigned to this Blodgett in some of the posts.