Bars fit saws, chains fit bars. Sean's information gives a great breakdown of the nomenclature that Stihl uses for their chain. To my knowledge, there are 5 different shapes of cutters that are available. They are Hexa, square ground, full chisel, semi chisel, and safety. These all refer to the shape of the cutting edges on the chain (they are chains, not blades). I won't get into Hexa or square ground because they don't really come into play with a 50cc saw. The other 3 types can all be sharpened with a round file of an appropriate size.
On a full chisel chain, the leading portion of the cutting edge comes to a sharp point. When correctly sharpened, this profile cuts faster than semi-chisel or safety chain. It's also very grabby, and the saw should firmly pull itself into the wood. Full chisel chain also dulls faster than the other two profiles so you need to sharpen it more often. I've always felt like it takes fewer strokes to get it sharp than when sharpening semi-chisel or safety chain, but if you want to get the full benefit out of it, you need to touch up a full chisel chain after every tank of fuel even if you don't get into any dirt with it. If you do get into the dirt with it, it will take more strokes of the file to sharpen than the other 2 types of chain. It's also the easiest type to tell whether or not its sharp because on a properly sharpened chain, the leading point is "cat's claw" sharp.
Safety chain is on the opposite end of the scale. The leading edge forms a large radius. The primary goal of safety chain is for the chain to be less grabby in order to reduce the chance of a kick back. The depth gauges also have a different shape to reduce kickback. The radius on the cutter makes it more difficult for the cutter to initially penetrate the surface of the wood. This reduces the chains ability to bite into (grab) the wood, which reduces the chains efficiency. It also spreads the wear across a larger area, so the cutters don't dull nearly as fast making it a better choice if you're cutting dirty wood. With that said, if you touch the ground with it, it still needs sharpened right away. However, if the cutters encounter small amounts of dirt embedded in the bark, a safety chain does not get as dull as quickly as a full chisel chain does.
Semi chisel is a middle ground between full chisel and safety chain. the leading edge doesn't come to a point, but the radius is much smaller than what's on safety chain. Its a happy middle ground that a lot of people like because its almost as fast as full chisel, but doesn't dull nearly as fast.
The gauge of the chain refers to how thick the drive link is. I can't remember what the common sizes are. I think they are 0.050, 0.058, and 0.0625 (or 0.063). This is the actual measurement of how thick the drive links are in inches when they are new. The gauge of the chain must match the gauge of the bar because it determines how wide the slot on the bar needs to be for that specific chain gauge. With respect to the gauge size, the saws drive sprocket or drive rim are universal and work for all gauge sizes. I've heard that if you start with a .058 bar and chain, that when the bar wears out (the slot becomes too wide) you can simply switch to .063 chain and keep going. I'm not sure how practical this is. Personally, I'd rather repair the bar so that I don't have several chains of the same pitch and length floating around that are of different gauges. To me, that seems like a good opportunity to get the wrong gauge chain on the wrong gauge bar and burn up a clutch or worse.
The spacing (pitch) on the drive links is another variable. The options are .325, 3/8, and .404. It literally refers to how long each of the links are on the chain. Smaller saws (40-55cc) often use .325 chain while saws that are over 50cc often use 3/8. .404 is more rare and is normally only used on big saws. The width of the cut (kerf) produce by chain pitch increases slightly as the pitch increases. That's why smaller saws tend to run .325 chain. Some people will run 3/8 on everything because they don't feel there's enough benefit to running .325 on their smaller saws to make it worth dealing with the hassle of having chains with multiple pitches. The pitch and gauge of the chain MUST match the pitch and gauge of the bar. The pitch of the chain MUST also match the pitch of your drive sprocket or drive rim, and each pitch requires its own diameter of file to sharpen the cutters. So switching from an 18" .325 chain to a 20" 3/8 chain requires you to switch the drive sprocket or drive rim on the saw and use a larger file to sharpen your chain. There are some bars that have a replaceable nose. My understanding is that when using such a bar, it's possible to switch to a different chain pitch and just swap the nose to match without replacing the entire bar. I don't run this kind of bar, so I can't confirm this one way or another.
There are also low profile chains that are used on really small saws like pole saws, and top handle saws. They have a narrower kerf and a shorter cutter, and are absolutely not the same as their standard counterparts. Low profile chains are a topic in and of themselves.
With 3/8 and .404 chain you can get standard (aka full comp or full house) chain, semi skip, or full skip. A standard chain has a 1 cutter for every 2 drive links. A full skip chain is missing half of its cutters meaning it has 1 cutter for every 4 drive links. Semi skip is in between having 1 cutter for every 3 drive links. Semi and full skip chains are useful on longer bars. They provide more room for chip clearance, and there are less teeth engaged in the wood at any given time which reduces the amount of HP required for the saw to pull the chain. Common practice is to use something other than standard chain on bars longer than 28" because when cutting wood that big you run out of room for the chips. If you're running a mid size saw (60cc-70cc) with longer bar (25"-28") its common to run some form of a skip chain to reduce the amount of HP needed to pull the chain, thus keeping your RPM up where the saw needs to be when its working. Switching from a standard chain to a semi or full skip does not require you to change any other component on your saw.
Your 261 has the same mounting bar pattern as a 661 (also the 290 series, 360 series, 380 series, 440 series, and 460 series), so they make bars over 36" that will physically mount to your saw. The problem is that the saw won't have enough power to run it, and its oil pump won't be able to pump enough bar oil to keep it lubricated. I know people who run a 20" bar on a 261, and that's about as big as I'd go. I'm not sure if the oiler will keep up with anything longer or not. Practically speaking, the oil pump is the limiting factor on how long of a bar your saw can run, especially if you running 3/8 chain since you can get that in semi or full skip.
Honestly, if you're in the dirt routinely, you need to change how you're doing things. The only exception to this is when you're trying to remove a stump, or at least cut it sub flush. Even then, I'd try to find a different option.
Hope some of this is more helpful instead of just more confusing.