By the by, here is how the official report plays out the initial collapse, essentially the same for both buildings based on my reading of the NIST report. Feel free to read the thing and correct this with a better understanding if you so choose.
Airliner impacts building. Collision injects fire and initial fuel into an office environment filled with other fuel, such as plastic, paper, and furniture, in addition to literally knocking the thin coating of spray on insulation from the structural steel. Simultaineous fires start in multiple floors of the building in wide sections of those floors, in addition to weakening the structure.
In the damaged sections, you have the remaining load bearing structure taking up the extra load from the portions that were destroyed from the collision.
Add to this extra load stress per column (both inner and outer), additional lateral (sideways) stresses are placed from expanding trusses exposed to heat. With the additional load, and weakened by fire, the hottest columns start exhibiting "plasticity" and begin to sag, pulling on the connecting floor, and pulling the face of the building inwards at the floor/wall joints.
Eventually, some part of the buildng gives way, and this instantly places more stress on the remaining structure, itself nearing limits of load/stress capacity. This results in a rather rapid collapse of nearby sections and simple physics do the rest.
Did the structural steel melt? No. You don't have to even get close to melting point to get loss of strength. Medieval blacksmiths didn't have near the ability to melt iron or steel, but could get it hot enough to work with hammer and anvil into swords, armor, horseshoes, and all manner of things.
Steel loses about 20% of its load bearing capacity at 300C, and some portions of the fires were hotter than that.