I am a new user and stumbled upon this thread because I'm having a similar problem. There really is a problem and the workarounds can get messy
Yes, there is a distinction between "schematics" and "sheets". Both of these concepts are generally available in other tools, so people are bringing the concepts with them, but it gets confusing because while KiCad has the concept of multi-schematic designs, it doesn't have the concept of multi-sheet schematics. The workaround is to use multiple schematics to implement multiple sheets, but this can be quite messy if there are a large number of connections between the "sheets" since they all must be represented with hierarchical connections, due to the sheets not actually being sheets of a single schematic.
Just to be clear, sheets are multiple drawings or pages that behave as one single schematic. A hierarchical design is composed of schematics (as KiCad currently supports), and a schematic is composed of multiple sheets (so far not supported in KiCad). The multiple sheets of a single schematic would share local names, the multiple schematics of an entire design would not. Ideally, one would use multiple schematics when there is a logical separation of functionality, and would use multiple sheets when you simply ran out of space on the current schematic, as an alternative to using increased page size.
This really is a pretty big shortcoming for large designs. I'm somewhat lucky, I generally don't need to print schematics on paper, so now that I know KiCad does not support multi-sheet schematics, I will just resort to using large page sizes to get around the problem. Some people do need to print out their designs for various reasons, however, and I can understand their desire to have reasonable page sizes and multi-sheet schematics.