Fly fishing is “regular fishing”, it’s just one of the many types of fishing techniques used.
That being said, the question appears to be whether or not a fly rod (there are many different fly rods, BTW) can be used with a spinning or casting reel. the answer is yes for the spinning reel and no for the casting reel. (The latter can be used, but it is very awkward.)
This is an ignorant question (Ignorant means lack of knowledge, it is not a pejorative) indicating that the person asking it is not a serious fisherman. That’s OK, most people are not that aware of the various styles of fishing.
For the most part, fishing rods are specialized. While different styles of fishing can be used in the same context, most serious anglers use the system that is most efficient for their needs. As a result, the rods for these systems are made differently from one another. If you are a casual angler and want to use the simplest system (other than a pole, which is the simplest but not a rod), then most people use spinning equipment. The reason this works out for beginners/casual anglers is that it has the flattest learning curve for casting. Most people never go beyond a float with a worm cast out hoping a fish is near by.
On the other hand, tournament anglers and serious species fishermen use the most efficient equipment they can get and that usually involves finding a system that works best for them. For example, fly fishing, which has the most difficult learning curve, is especially good for streams because it presents the lure/bait in the most natural and efficient manner. While other systems can be used there successfully, they are not as attuned to the circumstances . On the other hand, casting lures is more efficient in the context of a bass tournament (with some special exceptions) while walleye tourneys may use spinning equipment.
Serious carp anglers will use spinning rods that are in the 12 to 13 foot range. The list goes on.
Now to get into the weeds. You can use fly rod blanks for a variety of other types of rods, especially if you have to make your own rods to fit a specific style. In the US you can’t buy a quiver tip rod at Walmart, for example, or some of the other very specialized rods seen in Europe. (You can buy them at specialty stores online in the US or from Europe.). I chose to make my own from fly rod blanks. I was able to design travel rods from 4 piece blanks of the right sort.
I grew up in an angling family and one of my first rods was a short fly rod with a spinning reel. It was expedient but I moved on fairly quickly after it was clear that I would continue the family tradition. (Then they taught me to cast a fly rod after I mastered the casting reel.)
In the end, I learned to use the right tool for the job.