They are not the same, and actually, your question involves three separate products. Coconut milk, which is available canned, can be made at home by simmering one part water with one part shredded coconut until frothy, and then straining the liquid through a cheesecloth, squeezing out as much liquid as possible. Unsweetened coconut cream, which can be much harder to find canned, is made in the same manner, only the ratio is one part water to four parts coconut (milk may be used to obtain a richer product). Finally sweetened cream of coconut, which is used mainly for desserts and beverages, is a sweetened commercially produced version of coconut cream.
The names coconut cream and cream of coconut are used interchangeably. We’re guessing if the cake recipe doesn’t specify whether you are to use sweetened or unsweetened cream of coconut, you should choose the sweetened variety.