If you wanted a term which would be less confusing than calling continued pretraining ‘full-tuning’ or ‘fine-tuning’, I would suggest either ‘warmstarting’ or ‘continual learning’. ‘Warmstarting’ is the closest term, I think: you take a ‘fully’ trained model, and then you train it again to the extent of a ‘fully’ trained model, possibly on the same dataset, but just as often, on a new but similarish dataset.
If you wanted a term which would be less confusing than calling continued pretraining ‘full-tuning’ or ‘fine-tuning’, I would suggest either ‘warmstarting’ or ‘continual learning’. ‘Warmstarting’ is the closest term, I think: you take a ‘fully’ trained model, and then you train it again to the extent of a ‘fully’ trained model, possibly on the same dataset, but just as often, on a new but similarish dataset.