Technically yes, however being "cheap" has more negative connotations associated with it. Thrifty is more about "being careful" with money and using it wisely, whereas being "cheap" sometimes goes beyond just thrifty. However it's a subjective thing; one persons' "thrifty" is another persons' "cheap".
thrifty inexpensive low cost
Thrifty
"Thrifty" often has a more positive connotation than "cheap." Being described as thrifty implies being wise with money and resourceful, while being called cheap can suggest a lack of generosity or willingness to invest.
cheap, thrifty, moderate, plain
My dad was a thrifty spender. He was known for being thrifty.
Thrifty is a gentle adjective for 'cheap'. My grandpa was quite thrifty. Rather than pay for the bus, he walked everywhere and always smelled like sweat.
Yes, being thrify and being frugal are generally the same thing. They mean spending wisely, carefully, economically; not being wasteful with money or resources.
Thrifty
Economical, cheap, prudent, tight-fisted, frugal, stingy.
Just because you want to be thrifty doesn't mean that you have to be cheap! Would buying that car right now really be very thrifty?
Thrifty, cheap, picky, selective, pushy, assertive, haughty and proud.
thrifty, conservative, cheap, price-sensitive, economical