I am quite puzzled with these two terminologies. I know the basic meaning of metadata is "data about the data".
Microdata means the webpages are now more accessible to the search engines.
But what separates these two terms?
Microdata is the name of a specific technology, metadata is a generic term.
Metadata is, like you explain, data about data. We’d typically want this metadata to be machine-readable/-understandable, so that search engines and other consumers can make use of it.
In the typical sense, metadata is data about the whole document (e.g., who wrote it, when it was published etc.). This goes into the head element (which "represents a collection of metadata for the Document"), where you have to use the meta element and its name attribute (unless the value is a URI, in which case you have to use the link element and its rel attribute), as this is defined to "represent document-level metadata".
Microdata is not involved here.
If the data is about entities described in that document (or the entity which represents the document itself), we typically speak of structured data. An example for such an entity could be a product and its price, manufacturer, weight etc.
Microdata is one of several ways how to provide structured data like that. Others are RDFa, Microformats, and also script elements used as data block (which can contain something like JSON-LD).