Your tippet is the terminal end of a tapered leader, usually (but not always) the thinnest part, and generally governs the breaking strenght of your leader (assuming your knots are good). The "X" system refers to the diameter of the tippet material. 0x is thicker than 5x, which is thicker than 8x. Thicker than 0x, you get into the 0/ diameters, that go in the other direction: 0/1 is thinner than 0/2, and so forth.
Breaking strength is different for different materials anad brands. All 5x is the same diameter, but one may have a higher breaking strength, or "pound test" than another. One 5x tippet might be 4-pound test, one might be 5. It usually says right on the spool. For some kinds of fishing, the diameter is a more important index than the breaking strength, especialy fishing dry flies for trout, where you want a very small diameter.
Tippets are not graded by strength, but by diameter. By defination a 0x tippet is .011 inches in diameter. Each gradation of x is .001 difference, thus 6x is .005", and 3x is .008". There are also some #/0x definations around, and they work the same adding to tippet diameter, thus a 3/0x is .014".
Now, about the finest that one can draw monofilament is around .003" so a theoretical minimum tippet designation is 8x, but some manufacturers have stopped holding to the .001 defination, and are doing their own thing on tippets smaller than 7x.
Now, each size tippet from the same manufacturer is likely to break based on decending diameter, but across the sea of manufacturers tippets are not consistently breaking at the same tension.
And basically, fly fishing for trout has less to do with the breaking strength of the tippet, that the limpness of the tippet for a presentation. It is wholly inappropriate to fish a #20 griffith's gnat on a 2x tippet (you might not even get the tippet through the eye) as well as trying to cast a deer hair bass bug with a 5x tippet. One picks the tippet for the job.
Just get a range of tippets, 3x-6x work well for trout, 0x-3x is a good range for steelhead and bass, and use them proportional to hook size and conditions.
I have heard that you use a shorter, stiffer tippet when using fast sinking flies, like beadheads in streams. Is this the same for lakes?
I have an old Berkley fly rod that my Grandpa gave me. It has a sticker that says it's a Spartan SP-40. I can't find the line weight on it though. Does anybody know where I can find this information?
The short stiff leader for sinking flies is true, but one should take the species and their sensitivity into account. Basically, too long and limp a leader will not sink the fly with the line, when the line is a sinking line. This is when wanting a fly to drift along the bottom than drift at a middle depth.
With beadheads and body weighted flies the weight of the fly helps sink the fly so the leader can be longer and limper.
On a lake, it is better to fish a longer lighter leader as the fish can study the fly more than on a stream. And on the lake, if the line sinks faster than the fly, the fly will be drawn down by the line. It all depends on what you want, there are some circumstances when fishing a floating fly on a sinking line in a lake.