I just checked my detailed phone bill (I have Verizon) and text messages aren't detailed on there at all--only voice data is detailed. Obviously, other carriers will vary some.
The details listed on my bill are: the date, time, number, origination location, destination location, and minutes.
EXAMPLE
Date Time Number Origination Destination Min.
01/20 5:07P 123-456-7890 Myrtle Beach SC Incoming CL 5
01/20 5:08P 999-999-9999 Myrtle Beach SC WMyrtleBeach SC 5
The number listed in the number column is the number of the person I am communicating with for both incoming and outgoing calls.