Eugenics would be if the test was compelled upon pregnant women, with a forced outcome
Not necessarily — it's the overarching intent that defines eugenics as a philosophy/pseudoscience/practice, not the specific means, though in practice it would generally need to involve some kind of systematic implementation.
(And tho I disagree with ntmdino on right to terminate, I agree that terminating for Down's would be difficult to fit in a classical eugenic framework. But it's clearly part of the same ethical landscape, and in practice, many real-world systems of "eugenics" have tended not to actually give much of a shit about restricting their victims to people who could pass on "undesirable" traits.)
You could have policies that systematically drive low-income disabled people to penury and death and it not be eugenics, as long as it's not about "improving" the human stock, but instead just the belief that we're not worth what we might cost in benefits. Or you could have an actual system of eugenics that might look almost okay on the surface/at first glance — you could plan and carry it out through positive incentives and selective extra support for some, offers of contraceptive help and encouragement to use it for others, with no overt coercion or compulsion, and it would still be a form of eugenics, if the aim was to influence reproductive behaviour towards the goal of "improving" the human population genetically, however slowly.
That definition of eugenics is why I don't believe it's anything to do with eugenics if a woman were to choose TFMR. Even when her society creates conditions that may affect her decision (like availability of medical or financial support, respite, appropriate education, etc.), if the conditions aren't the result of a deliberate plan to genetically "improve" the population, it's not eugenics. Unnecessarily bringing eugenics and all its horrific baggage into someone's deeply personal decision is as irrelevant as it is cruel and disgusting, IMO.
If she lived in a society where her choice might be affected by similar outside factors AND those outside factors had been deliberately designed to try and influence her choices, towards a goal of "improving" overall human genetic "quality", then I'd consider that eugenics on the part of the system (NOT the woman), even if the woman made her choice in exactly the same way as a woman living in a system with the same outside factors but where they're the result of a shitty, callous system. I completely agree with this: a woman, using that knowledge, exercising her legal right to choose to terminate a pregnancy for whatever reason she damn well pleases - not even close to eugenics. A woman choosing TFMR actually can't be eugenics IMO. Even if her choices were to be influenced by conditions created by a system with eugenic goals — and even if the idea of passing down a genetic condition enters into her decision-making — she as an individual can't be carrying out eugenics. She isn't making decisions about a population, but about her foetus, herself, her family.
Essentially, I agree with you on everything else, but IMO it's potentially dangerous to confine the definition of eugenics to forcible testing, termination, sterilisation, because there are potentially more insidious ways eugenic intent can manifest.