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Yes, in some contexts, they're synonymous. However, they tend to have different connotations. Inexpensive usually implies low in cost, but of reasonable quality. Cheap tends to imply low in cost, and low quality. For example, someone cheaping out on a part.

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Yes, but apart from the case of a low quality and cost item ending up more expensive in the long run because of replacements and high maintenance costs; it doesn't tend to mean high in cost,low in quality.

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.

Things can indeed be both cheap and expensive. It takes two different perspectives, both being correct in their own right, and not directly contradicting each other.

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.

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