Before modern computers, the term computer was used to describe people who computed, and this term was indeed sometimes used as a job title or description. For instance, in an 1884 report of the U.S. Naval Observatory, a list of acknowledgements of assistance included these:
...Mr. Theo I. King throughout the year, in the grade of computer until April 20, 1897, and subsequently in the grade of assistant astronomer; Computer Frank B. Littell... Computer E. A. Boeger throughout the year; Computer G. K. Lawton ...
In fact the U.S. Civil Service had competitive examinations for the position of Computer. The 1890 test had sections on spelling, penmanship, copying, letter-writing, algebra, geometry, logarithms, and trigonometry. (The sample questions may be interesting to some.)
Computer was not just used for people, though; it came to be used for any tool which helped with computation. This was not just mechanical devices such as adding machines, but was also applied to sets of numeric tables and procedures published in books such as Screw Propeller Computer.
There probably was not much confusion when digital computers were coming into use, just as previously there was not a great deal of confusion between an adding machine, a book, and a civil servant. In the early years, computer was usually qualified by an adjective, e.g. electronic computer, at least at initial mention.
In the olden days of mainframes, from the mid 1970's to the mid 1980's, most people used real text-terminals to communicate with large computers. These real text-terminals were neither computers nor emulated text-terminals. They consisted only of a screen, keyboard, and only enough memory to store a screenfull or so of text (a few kilobytes). Users typed in programs, ran programs, wrote documents, issued printing commands, etc. A cable connected the terminal to the computer (often indirectly). It was called a terminal since it was located at the terminal end of this cable.
http://linux.die.net/HOWTO/Text-Terminal-HOWTO-1.html
Best Answer
My impression of semantic shift is the evolution of a word or term so that it is significantly different in meaning from the original sense. If that is the case, program, either as a verb or a noun referring to the operation of a computer, has not strayed far from the meaning attributed to the word since the 1800s.
According to etymonline.com, as a noun, program is derived from
While the computer sense is listed as beginning in 1945, a computer program is a definite plan or scheme for the operation of the machine. That type of usage goes back to at least 1837.
Similarly, etymonline.com describe the verb derivation
Again is suggests computer usage beginning in 1945. However, in 1889 program is used to mean write program notes which is what a computer programmer does. The meaning arrange according to a program from 1896 also seems pretty close to modern computer programming activities.
This sounds like old wine in new bottles.