I've often thought about the differences here, all 3 use heat based damage in a sense, but are treated differently, and I started to think why, and I think I might have an idea on why they perform different despite all being thermal based. This bothered me for a while, as how could these mechanically damage differently if they were JUST thermal energy? So I decided to brainstorm a little.
Incendiary is incredibly indirect, its a large amount of thermal energy without any real specific precision, and damage typically comes from large scale burns rather than incredibly powerful, directed burns, this means its generally unlikely to hurt any TRULY hard targets, but the large encompassing thermal energy could potentially flood any opening points inside the enemy, which explains why say, a cyber-disk might be effected by fire, as the flames and fuel might leak inside, and ignite the internals. Typically its a large, and sloppy ignition of fuel like gasoline or other incendiaries, which burns "hot" but not hot enough to melt anything substantial (usually) while also getting everywhere. However, besides pure thermal energy, there is nothing else to it for the most part.
Lasers are a velocity lacking direct beam of light energy : using a massively powerful beam of light which can burn / melt through many materials, and do more / less damage depending on the width of the beam, the power of the beam, and how heat resistant the material fired at is. However, despite the power, the beams have 0 kenetic energy, so armor which is stunningly heat resistant but fragile would still be viable, while armor with a high tensile strength and flexibility would be less viable if it cannot tolerate and dissipate heat. Besides that theres a possible issue of radiation : much like how sunlight can erode things that heat alone would not damage, there is a good chance of severe radiation particles which could damage tissue, fry electronics, or even cause metal to corrode / spark (like putting a spoon in the microwave) so even if something was entirely thermal resistant, the radiation. As a realworld example, light from welding is incredibly corrosive, and even if the light does not heat things up, having clothing exposed to this light for a significant amount of the time will severely damage it : so hypothetically one could even have a "heatless" laser which was room temperature, but fired intense radiation.
Plasma is like a marriage of kinetic weapons like bullets and thermal energy, firing out accelerated particles with excessive heat also involved. Because of the merge, its typically more effective than laser in most situations as it takes the heat, and mixes with particles, so the light, but heat resistant armor mentioned before would not be viable as the particles could still penetrate them with the high velocity. Theres also the issue of the anti gravity field which I assume could have effects on physics which bring in unforeseen issues with armor. However, the heat is less direct and splashes off of the particles more than the laser weapon as impact causes a dissipation of heat away from the impact site more than a laser would, meaning potentially armors resistant to ballistics but weak to lasers might face issues from plasma, unless heat itself would change how the material handles the impact, or the impact handles how the material handles the heat. Theres also a possibility that the intense speed, and single particle could cause an effect like in the LHC does, where particles impacting creates new particles (like the higs boson) which could wreck havoc which cannot yet be studies well by xcom, be it chemical changes in the target, corrosion, or even reforming the chemical composition of matter in ways which xcom might not entirely grasp yet.
Not sure if anyone cares about this, but it feels better to at least have a head-canon for why some things are better with lasers, others with plasma, and I wonder if maybe this makes sense with lore, or if I completely missed something on this : as far as I can tell this makes sense, though plasma weapons don't have much information on them that I'm aware.