The OS X Dictionary app's thesaurus lists "poor-quality" and "low-grade" and "shoddy" as synonyms of cheap. Merriam Webster's online dictionary gives this for definition 3a of cheap:
"of inferior quality or worth"
"of inferior quality or worth"
In fact, I've just looked at the OSX app, and "CHEAP" is the first word after the context in the "inexpensive" entry, and "INEXPENSIVE" is the first word after the context in the "cheap" entry.
http://www.merriam-webster.com/thesaurus/inexpensive http://www.merriam-webster.com/thesaurus/cheap
The relationship between the words,in the sense you describe, is hypo/hypernymy.
My original comment was in response to an apparent claim that the two words are entirely unrelated.
There can be different ways of looking at the cost of an item: 1) The cost of the parts and manufacture. 2) The retail price.
An item could be cheap from perspective 1 and expensive from perspective 2.