Fly lines developed from animal hair - typically horse - braided together, and then on to silk, and from there to man-made materials that continue to be updated and improved upon today. Modern fly lines use a variety of materials, but the main thing you need to know is that they divide into two main categories - Coldwater lines and Tropical lines. Cold water lines will often get sticky and don't hold up well in the heat, and Tropical lines can get brittle and coil up badly if it gets too cold. You don't have to worry about this too much for now; materials science has made cold water lines that hold up fine in all but the hottest climates and tropical lines that do well down to 40 degrees F or so.
The design of modern lines is often part of a marketing campaign, where companies battle to have the best niche lines. You'll see redfish lines, bonefish lines, tarpon lines, trout lines, bass lines... it goes on. These niche lines are interesting from a 'let's learn about physics' standpoint, and some of them really are pretty useful in certain scenarios. Click here for a glimpse into the kaleidoscope of taper designs.
However, all you need to worry about for at least the first year of your career is having a decent *general purpose line that casts well on your particular rod.* Learn to cast a general purpose line well, and then you can move on from there. Ignore the marketing hype.
There are many designations of fly lines. Some of these designations are objective, and these typically have to do with density - whether a fly line floats or sinks, and how fast. Floating lines need no explanation, but from there it goes Intermediate, Sink tip and Full sink. There are gradations of different densities between each of these designations, but we don't need to worry about that for now.
There was/is an arms race going on between rod manufacturers and line manufacturers. The message being marketed to us was ‘it's cool to have ultra stiff rods that can produce high line speed and throw a quarter mile’. Unfortunately, most humans cannot use these rods very well because the same characteristics that make them great for bombing line also make them difficult to cast well. People started 'up-lining' - say, putting a 6 weight line on a 5 weight rod - to help put a deeper bend in the stiffer rods and give more feedback to the caster. In response, line manufacturers started producing lines that were 'heavy' for the line designation, so like a 5 weight that is made to be 50% heavier than the American Fly Fishing Trade Association standard. Sometimes they'd tell you, sometimes they wouldn't. It got a little wild there in the late 2000's through the early 2010’s. Things have settled down a bit now, so they'll generally tell you when they've put extra weight in the line and since the pendulum has swung back they'll brag when they have a 'true weight' line now. As if that's an accomplishment.
Now, some people will argue that all weight forward lines are yet another marketing ploy. Here’s a fun question - Why don't we just turn the line around backwards when the end we are using gets worn out?
Short answer is - you can! For instance, I found myself in a real bind one time. I headed out to fish and when I got to the river I realized that I had grabbed a 4 weight rod, but the wrong reel... with an 8 weight line on it. While it's technically possible to make that match work, I was fishing for carp in clear water and needed all the delicacy I could muster to land a fly softly and accurately. So I figured well, the back end of the 8 weight might be a level line, but I bet it's approximately a 4 weight designation! I turned the line around on the reel - another reason to use loop-to-loop connections from your backing to your fly line - and proceeded to catch some carp. The lesson is that you can fudge it sometimes, if you've got the right puzzle pieces. Desperation helps, too.
The weight forward line has been around since the early 1970s I believe, but before that we had double taper and no taper lines. 'Level' or no taper lines are kinda sorta still around, typically in things like sinking lines that are dense enough not to need a taper and occasionally in niche lines for things like Euro nymphing.
It can be argued that double tapers (DT) are the best bang for your buck fly lines out there, because they really are 'two fly lines in one'. They taper from a heavy middle belly to two equal front tapers that allow for delicate delivery and good mending control. When one end wears out, you can flip it around and use the other end. You can even cut the line exactly in half and have two fly lines for short distance work - 40' and in - which covers most of what you'll be doing right now. I haven't personally used DT lines, simply because most of the fishing I did was sightcasting in saltwater or freshwater at longer distances. Now that I've moved to where creeks and 30 foot roll casts are the main ways to fish, I will be checking out DT lines.
Below are a couple diagrams that I ripped off the Internet that illustrate how modern Weight Forward fly lines work, and then an example of a Double Taper line. Both of these lines fish well, but you may learn that you favor one or the other in certain situations as you move forward with your career.
General purpose taper:
There are many styles of WF line out there, but the one below is pretty typical. Notice that the majority of the weight - found in the 'belly' of the line - is concentrated in the first 33 feet of the line. This is why there's a sweet spot for practicing your fundamental cast with about 30 feet of line out - that's where the line is going to load your rod the easiest while still not having too much line in the air for you to control.

Double Taper:
You'll notice that the weight is much more evenly distributed throughout the line than the WF design. This allows you to load the rod a little more quickly, but these lines are really at their best for casting and mending line at 40 feet or less. Fortunately, that's plenty far for most freshwater fishing applications.

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