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.