According to the National Geographic Education Encyclopedia webpage about continents, defines these as the main divisions of continuous land, extending out to the edge of the continental shelf - this also includes much of the surrounding islands. In the case of the division between Europe and Asia, this division is largely due to cultural differences.
The exceptions to this are what are referred to as 'microcontinents', that National Geographic site describes as being landmasses that are 'geologically distinct' from the neighbouring continents.
There seems to not be a consensus on a tectonics based definition of a continent; however, given that continents change over time, it is suggested in the article Continents as lithological icebergs: the importance of buoyant
lithospheric roots (Abbott et al. 1997) as implying that the particular lithosphere is "unsubductble' over two 0.25 billion year time periods - which, according to the authors, include mid-level and lower crustal levels, and that timeframe would also include Precambrian cratons as their core.