A SpatRaster represents a rectangular part of the world that is sub-divided into rectangular cells of equal area (in terms of the units of the coordinate reference system). For each cell can have multiple values ("layers").
An object of the SpatRaster class can point to one or more files on disk that hold the cell values, and/or it can hold these values in memory. These objects can be created with the rast method.
A SpatRasterDataset is a collection of sub-datasets, where each is a SpatRaster for the same area (extent) and coordinate reference system, but possibly with a different resolution. Sub-datasets are often used to capture variables (e.g. temperature and precipitation), or a fourth dimension (e.g. height, depth or time) if the sub-datasets already have three dimensions (multiple layers).
A SpatRasterCollection is a collection of SpatRasters with no restriction in the extent or other geometric parameters.