What's usually forgotten is what IBM was doing. IBM was slowly grinding their way forward into computers, as cost-effective products. They built the IBM 601 (mechanical multiplier), the IBM 602 (mechanical multiplier and divider), the IBM 602A (a 602 that worked), the IBM 603 (a vacuum tube electronic multiplier and the first commercial electronic computing product), the IBM 604 (a plugboard programmed electronic computer), and the IBM Card Programmed Calculator (at last, programs on punched cards). The IBM 600 series continued through the IBM 650, which was a real digital computer with drum memory. Donald Knuth learned to program on one. These were all real products with real business customers.
IBM had also had their DoD business. There was the IBM Defense Calculator, called the IBM 701. There was a whole series of expensive small-quantity vacuum tube machines sold almost entirely to DoD and DoD contractors. These were much closer to modern computers, but they were really expensive and didn't sell well. That part of IBM was mostly separate from the commercial side. In 1943, Thomas J. Watson Sr said "I think there is a world market for maybe five computers." He was thinking of the monster vacuum tube machines.
What really changed the industry was the UNIVAC I and magnetic tape. Again, it was memory, not compute hardware, that mattered. Eckert and Mauchly formed Eckert-Mauchly Computer Corporation, and built and sold the UNIVAC I. This was the first business computer with fast I/O devices - many spinning tape drives, all going at once. At last, you could get business-type work done. At last, fast sorting!
A UNIVAC I could directly replace huge amounts of IBM's mechanical card equipment. Which is what happened with one of the first customers, the U.S. Bureau of the Census. They had acres of rented IBM punched card gear at Suitland, MD. At the time, IBM didn't sell machines; everything was rented by the month. Census bought two UNIVAC I machines in 1951, and moved much punched card work over to them.
One day, the IBM sales rep was called in, and told that Census was terminating the rental on most of the punched card gear. This was a huge shock to IBM. Suddenly, large electronic computers were a real threat to the company's core business. Until then, computers had been seen as an additional business, but not a threat to the existing one.
In the early days of computing, there were "business computers", usually with decimal arithmetic and good I/O, and "scientific computers", usually with binary arithmetic and less I/O power. Business computers had to be cost-effective. Scientific computers tended to have government funding of some kind. The two lines didn't really come together until the IBM System/360.
That's the early commercial history of computers. The compute part was figured out well before the storage devices. Development of new storage devices resulted in huge jumps in capability. This is all pre-transistor; once transistors came in, the first step was to re-implement the existing stuff with transistors (IBM 709 -> IBM 7090, etc.) and then things really started to move.