Ah yes, I think you are getting the two mixed up.
As a very rough guide...
When you slump, you take solid pieces of glass (or fragments, or existing objects, such as bottles!), position them in a kiln (sometimes over a mould - as with the Chance handkerchief vases), and heat them until they melt (900 degs C or more). Then you switch off the kiln and leave it - and the finished object - to cool down evenly so that the glass anneals. In a commercial glassworks, the slumping kiln is usually open, so that workers have access to manipulate the pieces: for example, to push the slumped glass deeper into the mould, to get the precise shape that is required.
When you cast, you take some of your source of molten glass and pour/drop it into a mould, quickly do anything extra to it (such as make the hollow in rocco's ashtray in this thread) and, when it has firmed up, move it to an annealing oven (lehr) and leave it to cool (usually overnight).
You can buy glass kilns and moulds for use at home (not in the spare bedroom, I hope!).
http://www.warm-glass.co.uk/http://www.kilns.co.uk/etc
Float glass is deliberately made with a greenish tinge for windows, I've found out. My grandfather worked on a float glass bed at Pilkington's Cowley Hill Works in St Helens in the 1960s. Don't remember any of the glass being green then, unless it was deliberate "cathedral glass", so it's probably a fairly recent development.
"Green glass can not only absorb the heat but also reflects the infrared up to approximately 40% which can lead to a dramatic reduction in energy costs. Its pleasing greenish colour can reduce the transmission that results in unwanted glare and discomfort. Green glass reduces the transmission of ultraviolet light and subsequently minimizes the colour fading to furniture and flooring."
[from the Guardian Sunguard web site]