This isn't an answer, but please do not use propaganda and fake news interchangeably. Fake news is not the same thing as propaganda. They are sperate terms, albiet with overlap, but distinct terms nonetheless. Fake news is not a "new timey" word for propaganda.

There is no direct link between the two, both simply refer to the same mechanism and thus use the same word to denote it. As you noted in the question itself, the name of the ecclesiastical institution is 'Sacra Congregatio de Propaganda Fide' or 'Holy Assembly for Propagation of Faith' and the term 'Propaganda' was very informal and rarely used outside the ecclesiastical circles or people not involved or interested in missionary movement or Church administration. The term itself went into more common use in the last quarter of 18th century, along the development of modern political systems with increasing popular participation and prevalence of the democratic ideals and thus necessity to gather supporters. Throughout the 19th century the term 'propaganda' was generally understood as the act of presenting political stance or gaining public support for the particular cause (being more or less a synonym to what is called 'activism' today), but it began to gain modern connotations (i.e. manipulative information meant to warp the perception of facts through exaggeration, omission or even blatant lies) in the years leading up to the Great War and during the war itself. In the 1920s, the word 'propaganda' was generally used in the same sense it is used nowadays.

As u/ForsakenStation mentioned already, 'propaganda' is by no means synonymous with the fictitious information being presented as facts. The latter may be a part of the former as it can belong to any form of information system, but these two do not overlap. In general, propaganda, derived from the Latin verb 'propagare', meaning 'to give motion', or 'to put forth' (cf. 'propeller') denotes any information that is deliberately presented for specific reason, usually related to some specific goal. In practice, this form of information is rarely fictitious and most often simply does not discuss the issue in depth, presenting it unilaterally or only in rough detail, omitting any nuances. In some cases propaganda materials may even be devoid of any information the criterion of veracity can be applied to, simply influencing the intended target by imagery alone (Monument of Arminius erected near Detmold in Germany to commemorate Battle of Teutoburg Forest and by extension to symbolize German 'national power' is a good example of the latter). Although it is most commonly used in context of oppressive governments, it can be and is used by anyone and everyone, although in Europe and Northern America few would use the term openly for their content due to strong negative associations.