Microformats are an older type of structured data markup that relies on the class attribute of HTML tags to provide information about specific classes of entities that microformats support.
schema.org is a vocabulary that, unlike microformats, can be expressed in a variety of formats (syntaxes), including RDFa, microdata, and JSON-LD.
In essence, microformats combine a vocabulary with syntax, whereas for schema.org the vocabulary and the syntax used to express it are separate.