For various historical reasons, none of them justified, researchers seeking to intervene in the aging process have avoided talking about extending human life span. Until comparatively recently, and after a great deal of work on the part of advocates such as those of the Methuselah Foundation and SENS Research Foundation, the leaders of the research and funding communities actively suppressed efforts to discuss or work on the treatment of aging as medical condition. This environment gave rise to euphemisms such as "healthy aging" or "successful aging," and the goal of compression of morbidity: extend the period of health within the present human life span, but never, ever talk about trying to extend that life span. This has distorted the scientific endeavor, holding back efforts to develop meaningful rejuvenation therapies.
"Healthy aging" is a nonsense phrase. Aging is, by definition, the rise in mortality risk, the growth in systemic damage and failure of function. Aging is the opposite of health. Yet the phrase is well established and unlikely to go away any time soon, sadly. Any researcher or institution settling on the goal of healthy aging sets up for defeat before the work even starts. To pursue healthy aging is to accept aging rather than seek to defeat it. It is to aim at small modulations of the aging process, tiny adjustments here and there, rather than the sweeping change of rejuvenation. It is the assurance of failure, of missing the opportunity to change the world for the better.
Expressions such as "healthy aging" and "aging gracefully" signify that while the aging processes are making no exception for you, you're relatively healthy and/or the cosmetic signs of aging aren't as pronounced as they could be. This, of course, betrays the obvious reality that, in general, this kind of aging isn't the norm but rather a special case. If things were the other way around, you wouldn't find any articles stating the obvious fact that it's possible to age gracefully; rather, you'd find articles saying that disgraceful or unhealthy aging, however exceptionally, may happen too.
This choice of words is rather problematic, especially now that the dawn of rejuvenation is visible on the horizon. The terms "healthy aging" and "successful aging" really are sharp contradictions in terms. If you read the scientific literature on aging, most if not all papers giving general introductions to the phenomenon define it as a chronic process of damage accumulation or a progressive decline in health and functionality. If we try to replace these definitions in the two expressions above, the results are frankly hilarious: "a healthy chronic process of damage accumulation" and "a successful progressive decline in health and functionality". What's that even supposed to mean? Given that this progressive decline in health and functionality happens of its own accord and it invariably kills you, one would think that you really don't need to put any special effort in achieving it, and it appears to be "successful" enough without any need for external intervention.
It's of course good that healthy aging, as defined as a mitigated and relatively disease-free decay process, is actively promoted. However, this unfortunate terminological choice perpetuates the false dichotomy between aging and age-related disease; it reinforces the completely unsubstantiated belief that you can age biologically and yet retain your health. To put it bluntly, it's one of the reasons why you have people saying that when their grandfather died, at age 95, he was "perfectly healthy". If everything with him was in perfect working order, what did he die of, exactly? Some may think he just died of "old age", as if old age were a separate cause of death entirely, but that's not the case. Death by old age is just an expression to mean that he died of one of the many health issues that, in humans, generally manifest only after the seventh or eighth decade of life.
Just like the term "life extension" - albeit somewhat improper - has become a proxy for the application of regenerative medicine for the prevention of age-related diseases, so "healthy aging" and similar phrases have become synonymous with "being less sick than you could be", even though they really sound more like "getting sick in a healthy way". The only way to eradicate these misleading expressions is to successfully explain the true nature of aging to the public.