Difference between xs and xsd in XML schema file?

From the XSD 1.0 spec on w3.org:

The XML representation of schema components uses a vocabulary identified by the namespace name http://www.w3.org/2001/XMLSchema. For brevity, the text and examples in this specification use the prefix xs: to stand for this namespace; in practice, any prefix can be used.

in the end xs or xsd are only prefixes. XSD is used for example more by Microsoft schemas.

The important is how you declare the namespace.

<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema">
  ...
</xs:schema>

or

<xsd:schema xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  ...
</xsd:schema>

should be equivalent.

There is no difference, it is just a matter of choice

The xs: and xsd: are called namespace prefixes. They are declared using xmlns elements in the root element.

By convention people tend to choose either xs: or xsd: and map that to http://www.w3.org/2001/XMLSchema. Having both in a single document is confusing and should be avoided.

Check your xmlns declarations to determine what the namespaces are.