I read somewhere that, Henry VIII is credited with founding a "Regular Navy." I looked up the term in Google Books using the date of publishing filter, and it seems that the term is from early 18th century. So my questions are, how did the English Navy pre-Henry VIII differ from what is being referred here as "Regular Navy."? Were there administrative/bureaucratic differences? How do you tell the difference between "Regular" and "irregular" navies?
"Regular" in the context of a military force means that those elements are under the direct, official and permanent control of a state. On Land "irregular" elements normally indicates guerrilla activity. At sea, "irregular" elements might include privateers or vessels which are under direct control of the King only when his troops are embarked.
As for Henry VIII, English monarchs prior to him generated sea power when they needed it by conscripting or chartering vessels that were owned by merchants. Some monarchs did more than others to make this relationship sustainable, and they all were involved with fostering trade and merchant shipping to a greater or lesser degree. However, even the most successful kings who appeared to understand and foster seapower (Richard I and Henry V) never made it a practice to permanently create a large number of ships suitable for war directly under crown control.
Henry VIII is the first English king to systematically build purpose built vessels for the state military since the Norman Conquest. However Henry's Navy was still mostly composed of merchant vessels and privateers and his state owned navy did not have deep institutional roots. However the seeds of it had been sown and later monarchs would add elements like royal dockyards, cannon foundaries, and administrative structures which maintained the English (and eventually British) navy as a strong national institution.