Fillet welds with TIG seem more difficult that butt and outside-corner joint. TIG differs here from most other welding processes (as best I can judge as a recent starter). You could say "it's just TIG being TIG", but I will try to give a more enlightening exposition on the topic. Let's first restate what we mean by each joint type:
Fillet weld The horizontal / vertical fillet, what you would think of as a fillet weld in the "flat position", is like an upside-down "T". The vertical sheet rests its lower edge upon the planar expanse of the horizontal sheet as the metal is presented for welding. You weld, typically along just one side, leaving a triangular-cross-section fillet of metal which connects the horizontal sheet to the vertical sheet.
Butt weld is where two sheets in the same plane meet edge-to-edge and you weld along the length of the joint, fusing through the full thickness. Typically you would add some filler and aim to give a slight top bead and underbead. Adding 10% or 15% to the thickness beyond that of the sheet / plate at the middle of the weld, in a profile which rises in a smooth curve from the weld edge meeting the plate, would be the work of an expert.
Outside corner joint is where the plates meet at right-angles and you weld along the slight right-angled recesses formed by the plate thickness where the plates meet edge-to-edge in the inner corner. You aim to fuse and fill, leave a nice rounded corner joint, with a slight penetration bead forming an inner fillet.
Basically, the geometric constraint of working into the corner when fillet welding works for you with "stick" (SMA) and MIG. The meeting of the plates gives a simple aim-point for the arc which the weldor can follow exactly without concentration; the filler-metal is constrained and supported between two surfaces; and the requirement for penetration is easily met. Regarding penetration, you want some planar melting of the plate surfaces, but only a small amount compared to the full-thickness requirement of a butt weld. The "natural" penetration given broadly correct conditions is just right.
For TIG, on the other hand, the geometric constraint of working into the corner makes things more difficult. You have two plates to touch the tungsten electrode against by accident; you have to get the torch into the corner, get the filler wire under it from your left hand constrained into the corner, and incline your head to see where everything is under the torch. Then, assuming that we are TIG-welding because we want a neat small strong weld, we have to get the arc tight into the corner, meaning very little distance from the tungsten to the metal. This can mean that if the metal "races forward" because your weld is a bit uneven and you are picking-up temperature after running a bit cold and leaving a larger amount of filler, it can "wash" up to the tungsten. That sends you back to the grinding machine to re-dress your tungsten, having had to immediately interrupt your weld.
Continuing with TIG, finally to the issue of penetration. Oh yes, TIG has to be different again! The problem with TIG is way too much tendency to penetration when fillet welding thin sheet. TIG gives lovely deep penetration, which you can freely control and intensify, as you can freely slow down the weld and/or apply more power with the foot-control to up the penetration. You have this freedom to do so since the supply of filler metal is completely independently controlled in (absence of) relation to the heat input rate, making full-penetration butt joints easy. TIG doing the opposite thing to most other processes, as usual! When fillet-welding thin sheet, assuming you are using slow and concentration-intensive TIG (disadvantage) to get superlative joints (advantage), you don't want to melt through the full thickness of the sheet, resulting in ugly and strength/toughness-compromising oxidised melt-through defects. So you have to get the heat right down in intensity, while melting lots of filler metal as you have to add with filler the entire fillet cross-sectional area, but never-the-less have to do a "normal weld" in that you do get in close and melt the surface of the sheet.
All TIG is concentration-intensive, but within this general circumstance is in-detail another case of TIG being different and "inverse" to other welding processes.
Butt-welds of sheet metal using TIG welding could be discussed on its own. However, there is the chance here to discuss it in the context of all we have commented about fillet welding using TIG welding and / compared-to other welding processes such as "stick" and MIG. That is the opportunity being taken in the following comments.
TIG welding is often used to do butt welds of sheet metal and thinner plate with no gap between the sheets / plates at all. You can do that with TIG because as a welding process it has these two characteristics
The first point is pretty self-evident. You need to melt through the full thickness of the sheet / plate, hopefully with a weld pool which is deep in relation to its width in order to have a controlled weld pool and minimal contraction on solidification. So an inherent tendency to of the welding process to deep penetration is good.
The second point obviously has escaped an attempt to form a succinct point. This point is that with "stick" and MIG welding processes, the heat-supply-rate and the metal- supply-rate are coupled. Your welding rod (SMA) or welding wire (MIG) will melt in approximate proportion to your heat input, with only little room to tweak one at the expense of the other. So in the case of a zero-gap full penetration butt weld, which needs heat but very little filler, your wish-list for how you might control your weld is not going to be much met. The situation is totally different with TIG. You can supply absolutely zero filler while putting in heat, if you chose to. Usually some filler at least proportionally present in the current weld pool is desirable because it intentionally supplies deoxidants. Anyway, getting to the point for practical welding: you can start the weld by supplying heat for a period of time in one place, the start of the weld. You will add a bit of filler feed in quick small dips of the filler wire as the underbead forms, plus to make a generous domed melt pool, as it will flatten as it is drawn forward as you initially get underway welding along the joint. Your primary focus is on heat and the formation of a small penetrative weld pool, with addition of filler being a "trailing" reactionary consideration, providing for top bead and underbead about to be formed given the fluidity and onward development of the weld pool. It is usually OK to stop the progression of the weld to let the heat build-up if you judge that the weld needs local penetration, such as may be necessary if heat where being abstracted to nearby webs in the structure being welded, then resume motion when you are satisfied all is back in order. These assertions are illustrative. An expert would surely progress smoothly along the joint, adjusting the power with the foot-pedal as required to maintain the correct weld pool.
Well, I have found this endeavour absorbing. As a focused in-depth endeavour, it has taken me to the gym and the swimming pool for fitness, to get the most from my three-hour sessions at college. I have overcome a lot of obstacles and prioritised welding class in the face of other issues in front of bemused colleagues. So I hope there has been something to gain for you.