Relationship and differences between psychosomatic, somatoform and idiopathic disorders
This is purely all about terminology.

Somatic means of the body; bodily; physical. whereas the psycho part of psychosomatic refers to the fact that the somatic problem (symptom or disorder) is created through psychological means (with no medical evidence of a physical problem e.g. broken bone and/or torn ligaments).

Symptom refers to an observable behaviour or state, whilst disorder refers to a cluster of symptoms.

Somatoform refers to a physical symptom that cannot be attributed to organic disease and appears to be psychogenic (Dorland's Medical Dictionary for Health Consumers, 2007). 

Somatoform disorder refers to a set of psychosomatic symptoms (somatoforms) (Smith &amp; Józefowicz, 2012).

Idiopathic, as you pointed out is


  Of, relating to, or designating a disease having no known cause.


Further clarification

Psychosomatic is a word describing a somatoform.  A psychological problem is a somatised (Al Busaidi, 2010), and therefore is producing the experience of somatic symptoms, which are in fact psychogenic.

If a medical problem is considered idiopathic, the issue of whether it is somatic or psychosomatic is not determined. It cannot be both psychosomatic and idiopathic at the same time.

References

Al Busaidi, Z. Q. (2010). The concept of somatisation: a cross-cultural perspective. Sultan Qaboos University Medical Journal, 10(2), 180. Pubmed: PMC3074701

Dorland's Medical Dictionary for Health Consumers. (2007). Retrieved from: https://medical-dictionary.thefreedictionary.com/somatoform

Smith, J. K., &amp; Józefowicz, R. F. (2012). Diagnosis and treatment of somatoform disorders. Neurology: Clinical Practice, 2(2), 94-102. doi: 10.1212/CPJ.0b013e31825a6183