They are the same.I have the following information that I found from a short biography.
Jacob D. CONRAD is a son of William and Sarah (GILBERT) CONRAD, and grandson of Jacob CONRAD. The latter was born and reared in Pennsylvania, and died in Indiana, whither he had moved at an early day. William Conrad was also born in the "Keystone" State, and was taken to Indiana at an early day, and was there reared and married. He farmed in Elkhart, Noble Co., Ind., until 1877, and then moved to Christian County, Mo., where he still resides engaged in farming. He became the father of twelve children, eleven of whom are living: Edmund, George Freeman, John, Labrinthia, Jacob D., Anna, Angie, Matilda, Lottie J. and Barbara R. Jacob D. was born in Noble County, Ind., February 8, 1857. He remained with his parents until twenty-two years of age, and then began doing for himself. Since 1881 he has resided in Lawrence County, and has been engaged in the mercantile business in Aurora for three years. The following year he spent in working at the carpenter's trade, and in 1884 he was employed as manager of the lumber yard owned by R. W. Randall, and is also engaged in the insurance and real estate business. He has been quite successful since coming to Aurora, and is a pushing and energetic young man. Mary M. LOY, of Elkhart, Ind., became his wife in 1881. They have one son--Ralph. Mr. Conrad has a one-fifth interest in 640 acres of mineral land, a portion of which has been developed and promises to be rich in zinc, lead and silver. He is a member of the A.O.U.W., and in his business relations is obliging and courteous.
Notice that it says that William relocated to Christian County MO.I have found his gravestone along with several children in that cemetary.
I am currently trying to find more information on his father Jacob Conrad who was married to Amelia Fulk.Any further info would be great :D