A furled leader is a woven leader that has very good turnover characteristics to aid delicate presentation to spooky fish. I is durable and is mechanically more prone to behave well than a single fiber of nylon or flourocarbon which can kink or hold a bend (memory).
You don't need to use one to catch fish but you might learn to appreciate the subtle benefits they offer.
You shouldn't worry about using any kind of line you can get your hands on for tippet. If it knots well, does not put off the fish, does not break, and turns over nicely with a fly on the end then it's good tippet.
In some situations the tippet will exhibit a pronounced difference in strength and clarity - for instance fishing the flats. When big fish (like stripers) require 15# tippet using a second generation flouro lets you fish big tippet while being very stealthy at the sametime due to it's low vis.
This applies at a lighter scale to trout, a high quality tippet will be stronger and less evident to smart trout in a spring creek.
In general, use whatever is handy until you sense the need to use something better. If the knots break, the fish turn away etc - you have somethings to adjust. Otherwise you are doing well with what you have.
I go the other way too - if I think the fish don't care I dummy the leader down. For instance when fishing to bonefish near coral in a very remote area I will use 15# or even 20# tippet as long as they keep hitting the fly.
In the surf for stripers I use 20# maxima ultragreen for tippet and in that slosh the fish could care less. It makes much more sense when hauling a cow out of the waves too. Could use 30# no problem but the knot tying gets harder.
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