Yes the programs are similar and are made by the same company (so I've heard).
LT is uber simple. 3 shakes per day. Min 2 litres of water and only black coffee/leaf teas.
CD offers the SS (sole source) program which is almost identical to LT except that you get more choice of flavour and also bars.
Cambridge also has various other plans that do include food. For more information on CD you'd really be better off trying the CD forum as everyone on this forum is on LT... the CDers would be better equipped to advise you.