I think we are in danger of mixing up 'parkway' with 'park-and-ride' here, aren't we?
Surely they are the kind of inverse of one another? As (I think you) stated earlier, Bristol Parkway was originally intended for Inter-city passengers, to attract them to the trains with ample parking facilities but without the need to drive into Bristol TM or Bath.
The term Parkway (like, eg the GWR term 'road') was also meant to imply 'foot passengers for eg Bristol, do not get off here because you are miles from the town named and there may not be a bus!'
Park-and-Ride was a means to attract commuters or shoppers onto the train INTO the LOCAL town - not Inter-City travellers.
I have no idea really when the term Park-and-Ride came into use.
The first Park & Ride was what we now know as the Pear Tree Park & Ride on the outskirts of Oxford. It began some time in the 60s, initially on a trial basis, and permanent from about 1973.
In general Park & Ride has been for commuting into the local town, but as always there are exceptions. The trend around Oxford now seems to be towards more multi mode/function sites. Oxford's Thornhill Park & Ride has long been served by the coach services to London - there is a fair amount of out-bound commuting too. It also gets buses to the hospitals. And coaches to Heathrow and Gatwick Airports.
Bicester now also has a bus based Park & Ride that opened in 2015. It is most used for Bicester Village at weekends (there was some funding by the shopping outlet). But being operated by the county council it officially serves both Bicester and Oxford, being on the S5 bus route. In the week it is probably more used for commuting to Oxford in practice.
And the newest of Oxford's Park & Rides at Water Eaton is now also a multi mode transport hub. In 2015 Oxford Parkway opened on the same site with additional parking. Oxford Parkway and Water Eaton Park & Ride are effectively now one and the same; the Park & Ride naming has more or less disappeared as buses now show "Oxford Parkway" as the destination as does signage. I suppose "Parkway" is more recognisable to non-locals; a brand of the more generic Park & Ride term. One of 5 P&R sites serving Oxford, but only rail-served P&R.
What began as just another Park & Ride for Oxford city now has regular buses to the Oxford hospitals (John Radcliffe, Churchill, Nuffield Orthopaedic Centre) and Kidlington; also trains to Bicester and Marylebone (and now Oxford) as well. Since July there is a coach service to Birmingham Airport and now from December buses go to Woodstock and Blenheim Palace. Other buses go to Banbury and Bicester.
The common feature is plenty of secure parking facilitating the onward journey to the destination by frequent public transport, with the benefits of reduced congestion, better air quality etc. Parking is attractive - it maybe free or discounted, and there is good access from the strategic road network.
It doesn't necessarily matter if people are travelling in or out of town. As more routes are added then it can also become a transport interchange in its own right with more destinations available.