Is there any difference between 'valid xml' and 'well formed xml'?

There is a difference, yes.

XML that adheres to the XML standard is considered well formed, while xml that adheres to a DTD is considered valid.

Well-formed vs Valid XML

Well-formed means that a textual object meets the W3C requirements for being XML.

Valid means that well-formed XML meets additional requirements given by a specified schema.

Official Definitions

Per the W3C Recommendation for XML:

[Definition: A data object is an XML document if it is well-formed, as defined in this specification. In addition, the XML document is valid if it meets certain further constraints.]

Observations:

• A document that is not well-formed is not XML. (Well-formed XML is commonly used but technically redundant.)
• Being valid implies being well-formed.
• Being well-formed does not imply being valid.
• Although the W3C Recommendation for XML defines validity to be against a DTD, conventional use allows the term to be applied for conformance to XML schemas specified via XSD, RELAX NG, Schematron, or other methods.

Examples of what causes a document to be...

Not well-formed:

• An element lacks a closing tag (and is not self-closing).
• Elements overlap without proper nesting: <a><b></a></b>
• An attribute value is missing a closing quote that matches the opening quote.
• < or & are used in content rather than &lt or &.
• Multiple root elements exist.
• Multiple XML declarations exist, or an XML declaration appears other than at the top of the document.

Invalid

• An element or attribute is missing but required by the XML schema.
• An element or attribute is used but undefined by the XML schema.
• The content of an element does not match the content specified by the XML schema.
• The value of an attribute does not match the type specified by the XML schema.

Namespace-Well-Formed

Technically, colon characters are permitted in component names in XML. However, colons should only be used in names for namespace purposes:

Note:

The Namespaces in XML Recommendation [XML Names] assigns a meaning to names containing colon characters. Therefore, authors should not use the colon in XML names except for namespace purposes, but XML processors must accept the colon as a name character.

Therefore, another term, namespace-well-formed, is defined in the Namespaces in XML 1.0 W3C Recommendation that implies all of the XML rules for well-formedness plus those governing namespaces and namespace prefixes.

Colloquially, the term well-formed is often used where namespace-well-formed would be more precise. However, this is a minor technical manner of less practical consequence than the distinction between well-formed vs valid XML described in this answer.

Valid XML is XML that succeeds validation against a DTD.

Well formed XML is XML that has all tags closed in the proper order and, if it has a declaration, it has it first thing in the file with the proper attributes.

In other words, validity refers to semantics, well-formedness refers to syntax.

So you can have invalid well formed XML.

As others have said, well-formed XML conforms to the XML spec, and valid XML conforms to a given schema.

Another way to put it is that well-formed XML is lexically correct (it can be parsed), while valid XML is grammatically correct (it can be matched to a known vocabulary and grammar).

An XML document cannot be valid until it is well-formed. All XML documents are held to the same standard for well-formedness (an RFC put out by the W3). One XML document can be valid against some schemas, and invalid against others. There are a number of schema languages, many of which are themselves XML-based.

Well-Formed XML is XML that meets the syntactic requirements of the language. Not missing any closing tags, having all your singleton tags use <whatever /> instead of just <whatever>, and having your closing tags in the right order.

Valid XML is XML that uses a DTD and complies with all its requirements. So if you use an attribute improperly, you violate the DTD and aren't valid.

All valid XML is well-formed, but not all well-formed XML is valid.