There is a fundamental difference between frugal and cheap.
People who are frugal will shop around for an item before they buy, look at value instead of price, and try to find a trade item instead of having to spend money for it. People who are cheap will always try to get something for nothing, and if they have to buy it, will pay the absolute minimum.
Frugal is when you will recycle, repurpose, or take apart and salvage value from discarded materials. Cheap would be to not buy it at all or buy the least expensive item that will do the job.
Now the real difference is actually in the value. People who are cheap will buy the absolute lowest cost which is generally, but not always, an inferior product. Tools are a good example. Yes, you can buy a screwdriver that is less than a dollar, but it will not last and you will have to buy that screwdriver again and again. A frugal person will look for a better quality screwdriver so they will not have to buy another one. But they will not buy the most expensive one just because it is the top of the line, high tech, indestructible, titanium covered, engraved, or whatever.
There is something called a cost/benefit analysis. And frugal people can do it without thinking. Is the item worth the money it will cost to buy it? Will the item earn, either in time or repair costs, more that the cost to buy it? Will the cost to buy the item be recovered in usage? When these answers are yes, then buy them. Say you need to cut some firewood. You have an ax already, but you want a chainsaw. You visit a store that sells them. There are 5 models to pick from. One is small, lightweight, and very inexpensive, actually less than you expected to pay. Another one is big, heavy, and quite little bit over your budget, but it has a lifetime warranty. The three mid priced ones all have similar features, similar prices, and are good brands but they are nothing fancy. A cheap person will always buy the lowest priced item that will do the job. So they buy the small, lightweight model. They get it home and try to cut down a tree with it. It takes several tries to cut all the way through the tree and the user has to put a lot of pressure behind it to get it to cut through the knots. That will dull the chain faster and wear the motor out. So while that person didn't spend as much money for his chainsaw, he has to work harder and will have more repair time. A frugal person would buy one of the mid-priced saws. They are heavy enough to cut with out damaging the motor, and will probably be easier to use in the long run. If they had purchased the heavy, expensive one, it would probably be to unwieldy and they would wind up not using it as often because it is so difficult. Poor value.
Some people see the spending habits of the frugal folks as being cheap. But someone who is truly frugal will not buy things just to be buying them. There has to be a need and that need cannot be met by something they already have. Just because you can buy something, doesn't always mean that you should.