Why modern digital computers are often referred to as stored program digital?

Answer 1

Because they store the programs they are running in the same memory as they store the data that those programs are working on.

Answer 2

I haven't heard of that but with wording you used (stored "program" computers) I'm guessing they are two different names for the same thing. Program's are stored on computers, and are also digital. So, I'm not saying this is the correct answer but that's what I'm guessing.

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The terminology "stored program computer" is somewhat antiquated, although it does correctly describe all modern electronic digital computers as they store their programs in the same memory that they store their data in and can work on both with equal ease and speed.

The terminology "stored program computer" was originally created during the design and construction of ENIAC during WW2 to differentiate computers they hoped to build after the war based on the idea of storing programs and data in a common memory from ENIAC and IBM style punchcard unit record electromechanical equipment that were programmed by rewiring them and setting switches. The nonstored program computers and equipment were difficult and slow to reprogram and the process was highly prone to error. It was common to use removable "plugboards" (but ENIAC did not use them) to allow correctly completed programs to be quickly reconnected to the machine when needed again.

Some computers that were not stored program (e.g. Burroughs E101, IBM 305 RAMAC which introduced the first hard disk drive) were still being introduced in the late 1950s, but after the early 1960s as all new electronic digital computers were stored program computers the terminology has gradually faded from common usage.

Answer 3

Because they store the programs they are running in the same memory as they store the data that those programs are working on.