Your relationship is NOT a many to many relationship just because there are "Crows feet" on both ends of the relationship. FileMaker can only go by the field options specified. If you do not restrict a field in field options to unique values only or set it up as an auto-entered serial number, then it might be possible for this field to be the "many" side of a relationship as there is nothing at the data level part of your design to prevent the creation of duplicate values in this field. That does not mean that you can't design your user interface in such a way that only unique values are allowed for this field and thus it is actually the "one" side of a one to many relationship. It would then function just fine as a one to many relationship even though it is not labeled as such in Manage | Database | Relationships.
A true "many to many" relationship actually require either a third "join" table placed between the other two tables in the "many to many" relationship or the user of a "multi-value key" field--which lists multiple match values separated by returns in a single field.