There is no term for an XML parser that's restricted to a single schema because there's no reason for such a parser to exist. A nonentity needs no name.
To ask such a question indicates, perhaps, a lack of understanding of the difference between what's required to parse well-formed versus valid XML:
- An XML parser reads arbitrary XML and will report any errors that prevent the document from being well-formed.
- A validating XML parser goes one step further and will report any errors that prevent the document from being valid against a
given schema (DTD, XSD, RelaxNG, etc).
You may find additional checks being performed beyond what's expressed by a schema, but you won't find dedicated parsers being written to validate XML against a single, specific schema because the general case is already handled very well in both programming library and end-user application forms.
See also Well-formed vs Valid XML.