The active introduction of digital technologies by business entities does not only rapidly change their external and internal environments, but also affects the essence of the economy, forming qualitative structural transformations in it, which should be reflected in the terminology. The purposes of the work are to analyse modern approaches to the interpretation of the digital economy; to consider the conceptual and terminological situation in the management of an organisation; to propose a reasonable terminological set of concepts reflecting the gradation of management according to the degree of digital technologies application. The author has conducted the research within the framework of a systematic information and cybernetic scientific approach. Scientific methods, such as analysis, synthesis, generalisation, comparison, etc., are used. The data is taken from open sources. The author has analysed and summarised approaches to the interpretation of the digital economy, has grouped them and allocated as follows: technocratic, specific, scientific and industrial, industrial and sectoral, information and spatial, evolutionary. The article uses the generic concept “digital economy” and reasonably suggests a set of terms, such as “analog management”, “digitised management”, and “digital management” to differentiate the concept “organisation management” according to the degree of applying digital technologies. The paper shows the expediency of this gradation (including semantic content and terminological continuity), its integrity, completeness, consistency, and compliance with modern scientific knowledge. The author suggests using the introduced set of terms for various socio-economic phenomena, processes, and objects.