The relation between Rik and Saman is described in Chandogya Upanishad -Adhyaya 1 - verse 2.
एषां भूताना पृथिवि रस: पृथिव्या आपो रस: |
अपामोषधयो रस औषधीनां
पुरुषो रस: पुरुषस्य वासग्रो
वाच ऋग्रस ऋच :साम रस: साम्न
उद्गित्थो रस: ||2||
The earth is essence of all the beings ; Water is the essence of the
earth ;Herbs are essence of water ; Man is essence of herbs ;Speech is
essence of man ; Rik is essence of speech ; Saman is the essence of
Rik ; Udgita is essence of Saman .
In simple words Sama is Rasa or essence of Rig-Veda i.e. That is most essential part.
Explanation- Basically this mantra is meant for givings us the idea of Importance Sama-Veda and above all significance of letter "Om" "ॐ".This is explained by giving the examples.
Adi Shankaracharya in his commentary on the above Verse is explaining this mantra as thus.
Prithivi (earth) is the "Ashrya" i.e. residing place of rest of the
Bhutas i.e. elements.(Agni ,Vayu ,Jal etc.).
The "Aap" jal or water is essence of this earth. Because earth is full
of water. (Also water is the support of life on earth ).The essence of
water is "Aushadhi's" or "Food" , (because from the water itself food
and medicine's are grown) ,which keeps us alive and healthy. The
essence of these "Aushadhi's" or "food" is human body. Because our
body sustains on food and gets rejuvenated by food and medicine.
The important part or essence of this human body is "Vaak" i.e.
speech.(good speech). Because the good speech is "result of healthy
body and mind. The most important or residual part of all of the
speech is Rik (i.e.Rig-Veda) mantras. And the Saman or Sam-Veda is
even more refined part of Rik. i.e. Sama is essence (most important
part) of Rik mantras. And the ultimate essence of Sama is "Udgita"
i.e. Om (for Sam-Vedis).
We can read Chandogya Upanishad hindi with Shankar's commentary here.
We can also listen to a very good explanation of this Verse given by Acharya Satyajit Arya