How Can the No-Collapse and the Collapse Interpretations of Quantum-Mechanics Give the Same Description?

It is shown that no-collapse and collapse interpretations of quantum mechanics give equal object states (which predict everything that is observable) if one bases the relevant relations on the Von Neumann-L\"uders 'projection'. This connection is elaborated in detail from simple to most general cases. Distinguishability of the two approaches, which exists in principle, is also discussed. In the very simple illustration of passing one slit physical-insight difficulties in the collapse approach are indicated. For the purpose of interference between the two wavefunction components also the Maxh-Zehnder interferometer is discussed.