This article suggests that 'life satisfaction assessment could be considered a measure of quality of life':
Ferrans, C. E., & Powers, M. J. (1992). Psychometric assessment of the Quality of Life Index. Research in nursing & health, 15(1), 29-38.
https://www.researchgate.net/publication/21575378
I found this article that - understandably - a positive correlation between these two topics:
Yildirim, Y., Kilic, S. P., & Akyol, A. D. (2013). Relationship between life satisfaction and quality of life in Turkish nursing school students. Nursing & health sciences, 15(4), 415-422.
Articles such as these use measurements to reach conclusions.
I see life satisfaction as the individual's evaluation of his/her life as a whole, while quality of life refers to the level of general well-being. Both - I feel - can be represented on a continuum, but perhaps life satisfaction is more subjective, and can be affected by how s/he feels on a particular day, whereas quality of life is measurable and less fluctuating. But an individual's own assessment of his/her quality of life could also be subjective, and affected by mood, circumstances etc., so likewise be variable.
I sometimes feel that my own quality of life and life satisfaction vary according to how life is treating me! But rise or fall in the same direction.