Tomahawk HAD an ASM variant with the USN, but for a long time now that's not the case. Some say new tactical tomahawk is said to be able to be used on ships, but i haven't seen that confirmed by the USN.
Main difference between antiship missiles and cruise missiles is that antiship missiles are designed to search for their targets on their own. Cruise missiles, on the other hand, are fed with data where to go, and then they strike there. Some, like tac tomahawk and future versions of storm shadow etc can be redirected in flight, but that really depends on intelligence gathering, real time data processing and real time decision making abilities of the party that is conducting the attack.
Your typical lacm can't be used against a moving ship because it has no seeker that locks onto target and tracks it. it has electronics that help it determine where it is, and where it has to strike, but in most cases that is predetermined before launch. Even with tac tomahawk, i dont know if one could change the destination in real time, on a second by second basis. For a moving ship, only a several seconds delay could be the difference between a hit and a miss.