A couple of people here seem to have missed the point of why I'm asking this question. It's not because I want a tidy answer, a bunch of labels that I can stick onto pigeonholes; it's because it helps me to understand - and then to explain - the evolution of our sport as it went through the garagiste era of the 1960s and 1970s.
Ok, so I then have a try...
I think everybody here may have his own definition of what is 'private'/'privateer' and what is not. For myself I have spent quite some thoughts on this and came to the conlcusion, that there are plenty shades of grey, more than can be covered with two categories only. Also the meaning of words may be not exactly congruent in different languages, so this may also lead to slight variations in definitions. So first of all, the word 'Privatier' in German has of course a completely other meaning (somebody who has retired, living from what he has layed aside or some investments) and I think it could be similar in English. But as 'privateer' has a slight 'pirate-ish touch' I like the word very much and it seems common sense here to use it in 'our' context I can get along very good with that.
Again, for my personal taste, a 'private' team/driver and a 'privateer' are not necessarily all the same. The first has the meaning as acting 'independent' from the works, a category which can contain a lot of different forms of team organzations. But a 'privateer' in its strict meaning to me is a driver who operates his own car, usually with a comparatively small organisation. In some cases he has a wealthy patron or a rich lady to buy the car and enter it under his/her own name, but that doesn´t really change the case fundamentally.
Looking back in history I think the motoring world was separated quite early into 'gentlemen drivers' ("Herrenfahrer" in German) and 'factory drivers' ("Fabrikfahrer" / "Industriefahrer"). The first category were whealthy amateurs, who had found yet another playground for their sporting activities, while the other one consisted of 'professionals' - mechanics, chauffeurs etc. - who were under employment by the manufacturers. In fact, thinking about the real pioneers like Albert de Dion can probably be regarded as a combination of both, but the steps to separation must have started before 1900 already. For example I have read that when the drivers for the 1903 Gordon Bennett Cup were chosen, the German Automobile Club insisted on 'gentlemen' drivers, which included drivers from abroad, to avoid than being represented by members of the 'working class', as the Daimler factory had initially suggested.
The division was set forth by the introduction of the 'Grand Prix', which by definition was exclusive to works participation only until 1928. Therefore to me it is not precisely correct to subsume other events of this period under 'Grand Prix Racing', which to my understanding was only one category of motor sport and not congruent to 'Formula Libre Racing' (even if some of the latter events had the words 'Grand Prix' in the title).
But already in the 1920ies there were first occasions to further split the two basic categories. On one hand competitors like Eldridge, Halford or the Montiers may have 'legally' been 'manufacturers' (building their own cars made them eligible to participate in the official Grands Prix), but certainly not of the same class like Alfa Romeo, Delage or Bugatti, so usually we categorize them as 'special builders'. Decades later the BRP would perhaps also fall into this group which would be the explanation why they were refused with F1CA/FOCA membership by the more established 'garagisti'.
On the other side there were Bugatti, soon also Maserati and others, who offered their racing cars for sale, with or without works support on and off the race tracks, depending on whether the customers were willing to pay for this. Those who didn´t want to pay soon realized that they could save resources by forming 'racing associations' ("Renngemeinschaft" in German) with others on a peer-to-peer level, a step towards 'private teams', but still I would put them into my personal "privateer" category.
The development carried on when in the 2nd half of the 1920ies some of the independants/racing associations started hiring out their 'superfluous' cars to other drivers (Materassi, Nuvolari also perhaps). Some of the team leaders soon realized, that they were perhaps not as talented as their drivers, getting too old, or simply that running the team kept them too busy to carry on driving themselves, with Enzo Ferrari certainly the most prominent example. He was probably also the first to further break the divison between factory and private teams with his agreement to operate Alfa Romeo´s Grand Prix cars in place of an official 'factory team'. Similar concepts and arrangements I would categorize as 'works contracted teams' or maybe even 'exclusively contracted teams', depending on what kind of agreement is behind.
Thinking further there may be also a difference between teams like the Scuderia Ferrari in the 1930ies or Euroracing in the 1980ies (in both cases Alfa Romeo comissioned a team to operate the factory cars for them) or on the other hand Moser with Bellasi, Williams with de Tomaso, Lec with Pilbeam or Hill/Embassy Racing and later also Larrousse with Lola, when the teams commissioned a manufacturer to design and develop a race car model for their (exclusive) use.
Also there may be room for a 'semi-works' category, for example like the Scuderia Centro Sud with Maserati in the 1940ies, the Parnell team with BRM, Tyrrell with Matra perhaps in 1968 (not 1969), the Space Racing/Stockbroker March in 1973 or in more recent times Toro Rossi/AlphaTauri with Red Bull, Sauber (aka "Alfa Romeo") with Ferrari or Racing Point with Mercedes, who act/have acted more or less as "B(ackup)-Teams" in comparatively close cooperation with their main manufacturers.
Finally I could also think about dividing the 'private teams' further into 'fully independents' and 'customer teams', the latter with a certain degree of works support (like paying for regular service at the factory) but still operating on their own organization, in contrast to mere 'sponsorship entries', to which I would for example count the aforementioned Lec-Team of 1973, when to my understanding purley hired the factory March as a 'pay driver' with full works support...
Edited by uechtel, 09 February 2021 - 14:26.