The ways of misconstruing salvation in Christ Jesus are termed by the Congregation as Pelagian and Gnostic. As also noted, the use of these terms is done in a caveated manner. In other words, they are employed as a kind of doctrinal short-hand. The papal homily, which is the subject of the article, strikes me as a good exposition of what is meant in the document by a Pelagian understanding, at least from he perspective of practicing Christians:
A Christian who complains of not receiving a reward for going to Mass every Sunday and fulfilling certain obligations 'doesn’t understand the gratuity of salvation,' the pope said Nov. 7 in his homily at Mass in the Domus Sanctae Marthae.Why would anyone understand Mass as anything other than entering more and more deeply into the divinely-initiated dynamic of gratuity? In other words, participation is its own reward. What a rich reward it is! It is not what God will do for you because he's done an incomprehensible "amount" for you in Christ. Christ himself is the gift of eternal life!
'He thinks salvation is the fruit of ‘I pay and you save me. I pay with this, with this, with this.’ No, salvation is free and if you do not enter in this dynamic of gratuity, you don’t understand anything
Another, perhaps more secular way, of understanding salvation in what Placuit Deo calls a Pelagian manner is to think, "I am a good person. Therefore, God will save me." Not only is this presumption, it also implies that you're going to save yourself. This, too, is a way of refusing to enter into the dynamic of gratuity. In fact, believing you save yourself is to utterly refuse to enter into this dynamic altogether, preferring a pay-as-you-go approach.