Apologies for the delay in replying to your query which was:-
"if someone was listed as a 'slate quarry owner' for the Peak District area.... this was referring to ironstone specifically was it?"
We're getting into the complicated subject of Derbyshire's geology - geology being a very undertaught subject in schools! Which specific area of the Peak District are you searching in for a "slate" quarry? If I have this information I might be able fill in a bit more about the background information. Imagine the northern part of Derbyshire which is called the Peak to be domeshaped and mainly composed of limestone; to the west and east the gritstones followed by the coal measures consisting of layers of coal, clay (this is why a lot of potteries were found in coalmining areas as they used the local clay i.e. Denby, Langley Mill, Chesterfield etc.) and sandstones, overlay the edges of the limestone and dip westwards into Staffordshire and eastwards into the Notts/Derbyshire coalfield. As previously stated ironstone was also mined in the east and north east of Derbyshire, but these mines were not necessarily "slate" mines. Gritstone was quarried in the north, west and east of the Peak, and inbetween the gritstone and the coal measures are beds of sandstone and sandstone shales, which being laminated could be split along the bedding plane and sandstone slates produced. Also to the east of the coal measures (incidently all the rocks that I have described above were all laid down in the Carboniferous Era), are found deposits of rock called "rotten stone" or "Bolsover stone" which is formed from Permian magnesium limestone (the carboniferous limestone of the Peak District Dome is composed of calcium carbonate) and when first quarried looks to be a good building stone, but when weathered, erodes terrible - the Houses of Parliament were rebuilt of Permian magnesium limestone after it was burnt down in the 19th century, and has had to have drastic repairs to it in the 20th century. Slate is an metamorphic rock (which means it has been changed by heat by volcano rocks intruding or overlying the bedrock), from either of the other two types of rock i.e. sedimentary (which are laid down by water e.g. limestone, gritstone, coal measures, shale, mudstones, sandstone etc.) or igneous (formed from heat, i.e. volcanic rocks e.g. granites, basalts, dolerite, gabbro etc.) True slate such as Welsh slate was once shale (a sedimentary rock) changed by heat to slate. True marble is limestone (a sedimentary rock) having been changed by heat to marble. - I do hope I have not complicated matters.
However, the majority of people having hardly any detailed knowledge of geology tend to call limestone "marble" when it isn't, so you can see the confusion that could arise when describing perhaps a sandstone, or ironstone quarry when it was found that thin laminated beds of rock that were quarried made ideal stone slates. Thus such a quarry owner could correctly describe himself as a "slate quarry owner" without the rock he was quarrying being a pure slate such as Welsh slate, but a stone slate. I assume that you have found your ancestor (the slate quarry owner) on the census returns and that is where you've got his occupation information from.
Sorry if I've complicated matters, but will try and help you further with your query if I can. I've got many ancestors in the Peak who were lead miners; "brenners" who were lead smelters; "adventurers" who were lead miners who drove drainage levels (called soughs pronouned "suffs") to dewater lead mines; and a gt. grandfather who was a "marble mason" at Ashford-in-the-Water - he worked on the beautiful inlaid ornaments, tables etc that were so popular from the 18th century onwards (if ever you're in Buxton, call in the museum and view their Ashford Black Marble collection, it's the best collection I know). He called himself a "marble mason" but the rock they worked on was actually quarried and mined from beds of carboniferous limestone found near Ashford that when polished turned black, hence the famous name "Ashford Black Marble". I've obviously inherited these "rock" genes from all of these ancestors (some dating back to the 1500's), hence my great interest in geology, with me going caving and mine exploring in my youth. Sorry to have ranted on so much. Trust this helps a little in your research.