A folder is any container for files on a computer. A subfolder is simply a folder located inside another folder — the name emphasises its position in the hierarchy. Subdirectory means the same thing but comes from the command-line era (MS-DOS, Unix); it is still used in programming and technical documentation. In everyday language, when people say 'create a folder' they usually create a subfolder inside the current one. For example: 'I made a subfolder called Receipts inside My Documents' sounds natural; 'I made a subdirectory called Receipts' sounds more technical. Stick with subfolder for general writing and subdirectory for technical contexts.
Formed from the prefix sub- (from Latin, meaning 'under' or 'below') and the noun folder, which originally referred to a folded paper holder but was adopted for computer file systems in the 1980s. The term gained wide use with the graphical user interfaces of the 1990s, which displayed folder hierarchies visually.