The expression "biologically non-implausible"is a phrase I first heard used by Murray Shanahan at COGRIC (http://www.cogric.reading.ac.uk), in description of his work on cognitive architectures. In terms of the work of cognitive roboticists such as Shanahan, and many others, I think the term is perfectly suited.
The phrase "biologically inspired" is well known, and used extensively by a wide range of activities which carries out some activity, or process, in a way which takes some idea from a natural biological system - although the final instantiation often bears no resemblance to the system from which it took inspiration. And of course, there is no necessity (or obligation) for this: in this way, a task may be completed where it previously would have been overly complex. For example a number of search and optimisation algorithms inspired by the workings of an ant colony when searching for food/an alternative nesting site.
Onto the phrase "biologically plausible", and what you get is something with an entirely different connotation. This expression implies not just that this system or other is possibly instantiated in an actual biological system, but also that this system or other is likely to be instantiated in the actual biological system of interest. I've come across this statement in numerous articles and papers, although not necessarily so explicitly stated. So, for example, based on the activation of such and such a brain region when a patient performs a certain task, it is biologically plausible that this brain region performs function x. The use of the term in this context I think is perfectly justified. However, when it comes to building cognitive models - perhaps making a model of how a certain task is performed within the brain - I get a little uncomfortable with the term biologically plausible. This, to me at least (and I'm sure many may disagree), seems to overstate the significance of the created model. Such a model may well describe how a specific task is completed in the greatest detail, but to then say that it is biologically plausible, and then perhaps search for corroborating neural analogues for each processing, seems to overstate it. In my view, it would surely be unwise to claim biological plausibility for a model of a certain task in a specific domain, until it is known how this task fits in the context of the entire human information processing brain; perhaps there may be numerous ways in which such a task may be completed, none of which are intuitively possible until other aspects of brain function are enlightened?
And so the expression "biologically non-implausible". This, to me, implies that the presented statement, or system, lies within the realms of possible explanations for the functioning of the biological system, rather than being the most likely candidate. Basically, this argument boils own to emphasis - or more precisely, what point of view I perceive these two expressions to emphasise. Largely pedantic perhaps, but in my view an important qualitative distinction. I'm really just justifying why I like the expression "biologically non-implausible".