Barbara --
Since Co. "I" of Field's 1st Tennessee Regiment was the "Rutherford Rifles" from Murfreesboro, this is almost certainly the same man. You might be interested in the following web pages on this regiment:
http://www.first-tennessee.co.uk/origphotos.htm
http://www.williamsongrays.com/history_of_the_1st_tennessee.htm
Did you get this man's enlistment information from his service file?
You also mention that this man was killed at Murfreesboro, but died on different date. Could you clarify this? Did this information come from his service file, or somewhere else?