Yes, it appears that tandem and multi-junction solar cells are two terms for the same thing - two or more materials with different band gaps/absorption spectra layered on top of each other to capture more of the incident light than a single material.

http://www.oxfordpv.com/Tandem-perovskite-solar-cells

http://www.reuk.co.uk/Multi-Junction-Solar-Cells.htm

"Heterojunction" is a general term for any junction between two different materials - it can refer to transistors and other semiconductor junctions as well as solar cells. Tandem/multi-junction solar cells will necessarily include heterojunctions.

Thank you for your answer

Tandem solar cells are a special case of multi-junction solar cells, consisting of two different materials having considerably different band gaps (e.g., crystalline silicon and amorphous silicon). Other cases of multi-junction cells are triple cells (e.g., Ge/InGaAs/InGaP) and quadruple cells (e.g., GaSb/InGaAs/GaAs/AlGaInP), where all materials have different band gap energies. Triple and quadruple cell types are typically used in concentrator photovoltaics.

A single-junction cell can contain hetero junctions as contacts; this concept is used e.g. by the company Panasonic for their so-called HIT cells (originally developed by Sanyo).

Hi

Tandem solar cell: Monolithic stacking of two simple cells.By combining two cells (thin layer of amorphous silicon on crystalline silicon for example) absorbing in related spectral fields, one improves the theoretical yield compared to distinct simple cells, which they are amorphous, crystalline or microcrystalline.

Multi-junction: The cells multi-junctions consist of several thin layers.A cell triples junction, for example.Each type of semiconductor is characterized by a maximum wavelength beyond which it is unable to convert the photon into electric power.On another side, into on this side this wavelength, the surplus of energy conveyed by the photon is not converted into electricity.From where interest to choose materials with lengths as close from/to each other as possible.

The more cells you have in a series arrangement, the more spectrally sensitive the device becomes. It is easily possible to make a 4 layer cell that works fine in the sun and doesn't work at all under artificial light especially fluorescents. Yet even the 4 layer cell optimised for noon conditions will perform very badly in the early morning or late afternoon.

A tandem solar cell is a multi-junction solar cell. By definition, a tandem cell combines 2 cells, in series or parallel. If you use a two-terminal tandem configuration, it is a true example of a multi-junction solar cell too. In the case of four terminal tandem, where two distinc cells are stacked, it may not fit into the definition of a multijunction. Here is where a tandem differs from a multijunction.

What I understood while i was searching for an answer to this exact question, is that the main difference between a tandem SC and a MJSC is that the first is a MJSC with two layers, while other MJSC might consist of more than two layers.

Helpful comment from Jan-Martin Wagner.