What is the difference between being frugal and being cheap?

The fundamental difference for me is the ability to recognise value/quality.

Consider how a frugal vs cheap person looks to buy food with $10:

• A frugal person who cares about nutrition will buy the most nutrient dense foods, and cook a nutritous meal at home for 2. It would likely not be meats/seafood, so a conservative person with a $10 budget would think about what would give the most nutrition for his buck.
• A cheap person can use $10 to buy the most food, for eg, 20 packets of chips. Gives alot of bulk, but no nutrition.

Likewise, for clothes:

• A frugal person would consider Cost-per-wear
• A cheap person would buy the cheapest thing, without consideration for quality.

Being cheap is looking at price without any justification. It could also mean just buying something purely for its price and not looking at its quality, its uses for yourself, and how long the item can last, whether it suits your needs.

Being frugal is only buying what is needed (like toilet paper offers, dettol with 3 for price of 2, other consumables with long expiry date) and looking for the best deal available in the market to match what you need.