Is the law of flotation the same as Archmede's Principle? If not what is the difference?

The law of floatation is that a floating body displaces *its own weight* worth of the water in which it floats.

If it is not large enough to displace its own weight worth of water, then it will not float.

This can be worked out using Archmede's principle. (which is broader).

Archimedes principle states that the upward boyant force on a body in water, is equal to the weight of the water it displaces.

i think there does not exist any law called law of floatation . there cannot be any particular specifications which a body full fill then it must be floating and by how much of of it immersed in water. just learn the exact definition and apply it to the problems and you will know whether the body will float or not :)