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The concept of triplet of Hilbert spaces is a special type of rigged Hilbert space and is due to Yu. Berezanskii. Motivated by a bunch of problems in the spectral theory of boundary value problems, spaces of analytic functions, and singular integral operators, a genera- lisation based on the concept of closely embedded Hilbert space has been obtained by P. Cojuhari and the speaker. In this talk, we compare this generalisation with the generalised triplet of Hilbert spaces in the sense of Berezanskii by showing when they coincide, when they are different and when, starting with one triplet, we can