Yes and you can hammer in nails with a crowbar, or you can pry things apart with a claw hammer, they're both made of tool steel so they're the same thing in a sense and if crowbars were cheaper than hammers you could build a house using crowbars instead so the market would have to take that into account.
Yes FPGAs and GPUs (and CPUs and ASICs and...) are made of silicon and comprised of logic gates and other various elements, and yes they can do some of the same tasks. Yes you can make a GPU (of sorts) out of an FPGA but you cannot make an FPGA out of a GPU. The FPGA is a massive digital breadboard that you can "wire" into any sort of digital device you want, THAT is what makes it so powerful, it is versatile, it is flexible, a GPU on the other hand is a hardwired device, it will always be a GPU, it is a microprocessor, it cannot do anything at all without code and you can never change what it is, you cannot add a new instruction or tweak an existing one to work differently, the design is cast in stone.
An FPGA is a block of clay, a GPU is a ceramic mug. You can make a mug out of a block of clay, it probably won't be as nice as a mug you can go buy from the store but you can make it exactly the way you like, precisely the dimensions, shape and design you want, your imagination is the limit. You're not limited to a mug either, you can make a vase too, or a flower pot, or a floor tile, or a trivet to set hot pans on, or a candle holder, a sculpture, or if you're like some of the kids in my Ceramics class in highschool you can make a bong and hope the teacher doesn't realize what it is. Blocks of clay are not really competing with ready made mugs, making your own mug will probably cost more, depending on your skill it will probably not turn out as nice, and it will certainly take a lot more time and effort but in exchange you get the flexibility to make whatever you want, to specify every detail, to tune and tweak the design in any way imaginable.
Maybe you need one very special mug designed specifically for some very unique need that will never be made in volumes sufficient to have them mass produced, or maybe you have an idea for a new type of mug that you wish to test out in the field before committing to the considerable cost of manufacturing a batch of tens of thousands of them, THAT is what FPGAs are good for, and THAT is what people pay the money for. If they need a GPU they buy a GPU, but a GPU is useless if you need something that doesn't involve mathematical calculations of the sort used to render 3D images.