What is the difference between an ORM and an ODM?

An ORM maps between an Object Model and a Relational Database. An ODM maps between an Object Model and a Document Database. MySQL is not an ORM, it's a Relational Database, more specifically, a SQL Database. MongoDB is not an ODM, it's a Document Database.

MySQL is an example of a relational database - you would use an ORM to translate between your objects in code and the relational representation of the data.

Examples of ORMs are nHibernate, Entity Framework, Dapper and more...

MongoDB is an example of a document database - you would use an ODM to translate between your objects in code and the document representation of the data (if needed).

Mandango is an example of an ODM for MongoDB.