Recent analyses of the potential effects of advanced technology on jobs has tended to focus on possible reductions in routine cognitive white-collar jobs due to computer algorithms and in blue-collar jobs due to robots and factory automation. This paper provides a different perspective on the possible future of work by: (1) measuring changes in job attributes/tasks from 2005 to 2015, straddling the boundary between the pre-AI and AI eras; and (2) decomposing those changes via a shift-share analysis into the changes that occurred within occupations and changes in the shares of employment between occupations with different characteristics. Our primary source of information on job characteristics over time is the Occupational Information Network (O*NET) database developed by U.S. Department of Labor's Employment and Training Administration. While prior research has used O*NET data cross-sectionally, we create a new panel dataset that allows us to analyze changes over time for 170 job characteristics from four O*NET questionnaires completed consistently by workers (job incumbents) since 2003. Per our title, we find that within-occupation changes dominate, raising doubts about the ability of projections based on expected changes in the occupational composition of employment to capture the likely future of work. Indeed, our data show only weak relationships between automatability, repetitiveness, and other job attributes and changes in occupational employment. The results suggest that analysts give greater attention to within-occupation impacts of technology in assessing the future of work.