As well, when did this term come in popular use, rather than ironclad, protected cruiser, and so on?
Yes, ships like Mars were referred to simply as battleships. In 1887, the Royal Navy carried out a major reclassification of its ships; ships that were built to fight in a battlefleet were reclassified as battleships, while those that were intended to protect trade, scout, or raid shipping lines were reclassified as cruisers. The term battleship had been used somewhat before then. It was a contraction of the older 'line-of-battle ship', and in this sense is attested to as early as 1794. In the 19th Century, most of the ships that would later be classified as battleships were referred to as ironclads in a general sense. More specifically, they were given names that described their capabilities. Ships like Warrior were broadside ironclads, while those which had a few fixed guns mounted centrally (like Hercules) were central battery ships. The low-freeboard turreted ironclads like Glatton were coast-defense ships, while larger ones were classified as turret ships. These larger ships were also described, from time to time, as battleships. In October 1887, the classification 'battleship' was officially introduced. There were several subclassifications within that; the most modern, largest ships were 'first-class' battleships, forming the core of the battlefleet. Older, less capable ships were 'second-class' ships, and were typically used to provide extra muscle on colonial stations, as they were still capable of destroying cruisers. The oldest ships, like Warrior, were 'third-class' ships, and tended to be kept in reserve.