Nudribranchs and cucumbers are two totally dufferent creatures. Cucumbers belong to the phylum Echinodermata, which includes sea stars, urchins, sand dollars, crinoids, etc., while nudibranchs belong to the phylum Mollusca which includes clams, snails, sea hares, octopus, etc.
I am not sure on the care of your particular nudibranch, but be careful because many feed off of cnidarians (corals, anemones, hydroids). Keep a close eye on your corals. Interesting sidenote: the word nudibranch means "naked gills" and refers to the small tuft of cirri on their back that serve as their gills.
As John said, they are very different creatures. It would be the same as saying you (as a human) are the same as Acropora sp. That is how different they are.
The tiger tail cucumber is a sand sifting cucumber, it picks up the sand with its tentacles then ingests the biofilm that covers it. Then out the other end comes some small pellets of sand. They are good to keeping the surface of the sand bed "clean".
As for the nudibranch, well that is very difficult to say. All nudibranchs have a very specific diet, such as sponges, hydroids, corals, bryzoans etc. Which one they eat for many species is not known. Before any guess can be made to what the "blue nudibranch" eats you would need to get a positive ID on what species it is. The best chance to find out what it eats though is to watch what it consumes on the live rock within a reef tank. Problem with nudibranchs is because of their very specific diet it is unlikely to be able to have it self sustaining in a small aquarium, i.e. enough sponge/hydroid etc be able to continually grow to keep the nudi fed.