There are quantitative not qualitative differences between the concrete and the mortar. At meso-scale, the mortar can be considered as a composite material with three phases: cement paste, aggregate and the interfacial transition zone (ITZ) between them. These phases are similar to the concrete phases at macro-scale regardless to its ingredients. It seems for me that it doesn't matter to call the mortar as "concrete" if the full information about the mix proportions (details of mix design ) are provided.

Regards

Forgetting about what we see in classical text books, I see no difference between concrete and mortar. From structural point of view, their durability and macro mechanical behaviors are important rather than their ingredients. All bendable concretes (ECC) are actually bendable mortars as there is no coarse aggregate in them. But the term concrete is well accepted for them. Moreover, many self-consolidating concretes have no coarse aggregate to achieve the required viscousity. Again they are actually mortars but the term concrete is widely used for them in both research and practice. Other examples are lightweight EPS concretes (with no aggregate), autoclaved aerated concrete (AAC), etc.

the main diffrence is that the maximum size of aggregate(gravel) that is used in concrete mix much larger than the aggretates used for cement morter. but it is common to highlight the difference using different terminologies.

The question is complex as the classification and terminologies of the materials are largerly function of the standard, country, etc... Most of the times more specifications are needed to make difference between materials with similar terminologies.

Concrete is a mixture of a binding medium,fine aggregate,coarse aggregate , water (and admixtures.If the binding medium is cement, the product is known as cement concrete. Similarly,if the binding medium is geopolymer  (alkali activated fly ash etc) it  known as geopolymer concrete.Hence, using the term concrete to describe  foamed mortar is not appropriate.

In mortar and concrete one has aggregate and the difference between the aggregate using in each is the size. So the terminologies regarding mortar and concrete will be always subject to debate.

This is as important as standards regarding concretes and aggregates are not uniforms through out countries