TRADITIONALLY, muslin was also known as 'cheesecloth' and was used to sieve the whey out of fermented coagulated milk, leaving the curds for making cheese. However, like so many words the meaning has become distorted. If you go into a traditional haberdasher or cloth shop, you'll most likely get the very thin, very open weave stuff you've already encountered. Elsewhere, you could get just about anything. The essence is that the warp (lengthwise threads) and weft (crosswise threads) are of equal thickness.
CALICO, again traditionally, is a plain, unbleached cotton fabric which may contain cotton husks and/or 'slubs' (basically, lumps in the weave). It is usually quite a bit heavier/thicker than other common cloths. Similarly to muslin, warp and weft are equal thickness so there is no pattern to the cloth, just plain flat material. (The self-colour pattern you see in some formal shirts is created by the use of different thread thicknesses - it also accounts for the 'pattern in rip-stop nylon where a thicker thread occurs at regular intervals in both directions)
IF you are thinking of dying your background, then a cotton fabric is a good option as it absorbs the dye rather than it sitting on the surface as happens with man-made fibres. If painting, this is less important although usually cotton duck (aka light canvas) is used for this as it is more crease-resistant and you don't want your paint cracking off!
I've made a couple of 9ft wide backgrounds from calico (yes, it's available in 108" width) and there are a couple of points which you should be aware of if you go this route.
- When you wash the calico prior to bleaching/dying/whatever it absorbs a LOT of water and becomes surprisingly heavy. Natural fibres typically absorb about 97% of their own weight in water. Don't try doing it in your domestic washing machine - it'll probably cost you a new machine!
- When your large piece of calico is bleached/dyed/whatever and has been rinsed, DON'T tumble dry it completely. If you do, you will spend about 10 SOLID HOURS ironing the creases out before it's fit to use. I'll leave it to your imagination how I know this

I would rate this ironing as the MOST BORING thing I have ever done - and I've had to do some pretty boring things in my life, believe me. It's also darned hard work!
Curtis is almost right - but you
can find truly opaque material. It's called blackout cloth. Typically it'll have about 140 picks per inch
(threads in each direction) of very thin thread. Guess what. It's expensive. It's also not easy to find unless you live right in the middle of a textile area (you know, the one which bought the majority of that lovely Australian Merino wool for a couple of hundred years).
Probably your optimum realistic route would be to get the widest material of bedsheet weight and weave and work on that. It may take a bit of hunting down, you may even decide to buy ready-made backgrounds. But there's a lot of pleasure
(after you've finished, maybe not during your work) in producing images using something you've made yourself.
Good Luck!