great answers on limestone streams, but the question also asked 'bout freestone streams, and there's more to say about the differences.
Classic limestone streams have not only spring water that moderates water temps, but they may also have have actual limestone geology that acts to neutralize acidic water from decaying plants. The fertile/less acidic water in some limestone creeks may hold more subsurface and surface insects, and potentially more fish, and bigger fish.
Some freestone streams that drain swampy or hemlock-dense areas have tannic, more acidic water, and little limestone in the geology to neutralize the acid. A freestone stream like this is infertile and has less insect life relative to a classic limestoner that has both springs and acid-reducing limestone geology.
There will be fewer bugs and smaller fish in a tannic mountain freestone stream than a classic limestoner. Also, the fish in a tannic mountain freestone stream are less likely to be brown trout, and more likely to be brook trout, which evolved in colder forest water and better tolerate tannic water.... (note: there are limestoners with brookies, but there may be few brown trout in tannic streams that have a lot of brookies)
If a freestone streams drains undeveloped mountain land without limestone geology, it may be cold enough to have a good population of smallish brook trout (up to 10 inches, usually smaller). If so, it can be fun to fish with dry flies _because_ it is relatively infertile -- the lack of subsurface and streambred surface bugs leaves the fish with a summer diet heavy on bugs that fall in the water! Toss a dry fly... smack. Sometimes two fish clear the water trying to grab it.
Not much point in fishing flies that resemble subsurface watercress-dwelling insects in a tannic infertile mountain stream, because those bugs aren't there. (Still, fish in infertile streams have to be opportunistic, so they might hit whatever you toss 'em.)
But on a classic limestoner, sinking flies that resemble the subsurface "cress bugs" that the bigger trout gorge on may be the way to go. (see watercress comments above) The water may be clear, and the fish may be wary. I've had fish emerge from the undulating water weeds of the classic PA limestoner The Letort and smack a dry fly, but they have stuff to eat below the surface and can be tough fish to catch.
Great thing about this part of the country: we have nice stream examples that range from fertile classic limestoners to infertile brookie mountain tumblers.
Sometimes freestone versus limestone fishing can imply a change of scenery: at the extreme, mountain (freestone) versus meadow (limestone).