Good review but "qualitatively different" is a bit of an understatement.

tl;dr: Chernobyl/RBMK reactors are inherently dangerous in nuclear design and in operation without suitable containment structures, unlike Western reactors like TMI or Fukushima.

TMI and Fukushima are comparable to a degree but it is important to note that TMI is a Westinghouse pressurized water reactor whereas the Fukushima plants are GE boiling water reactors. TMI had a LOC event due to a stuck pressurizer vent valve that went undetected after a reactor scram which, combined with incorrect assumptions in the operating procedures, led to a core melt. Fukushima experienced station black out which means loss of both offsite and backup power. The reactors shutdown and operated as designed for this scenario but the design basis assumption is that power would be restored in 4 or 5 days (don't know the exact number). It actually took more than a week to restore power due to the devastation of the earthquake and tsunami. Core cooling was maintained by discharging steam into the containment cooling pools but this method can not be run indefinitely and as the pools overheat it threatens the containment. Without a source of power the H2/O2 recombiners could not safely burn off the hydrogen which led to explosions of the reactor service buildings.

In contrast, the RBMK reactors are graphite moderated but water cooled. The reason for this design was they were developed for civilian power generation by scaling up military reactors used for plutonium production for nuclear weapons (graphite moderator allows fuel extraction without shutdown). During low power operation, the RBMK design has a positive reactor power void coefficient. What this means is that an increase in power lowers the density of the water coolant which allows more neutrons to escape into the graphite moderator where they are slowed down and thus split more atoms. In other words these reactors have an inherently dangerous operating region where an increase in power can lead to more power in a positive feedback cycle. This is what destroyed the Chernobyl reactor. (Note that water moderated reactors such as TMI or Fukushima have a negative power void coefficient where an increase in power reduces the density of the coolant and moderator which allows neutrons to escape the core without causing a fission thus dropping power, the opposite of an RBMK)

Of course the designers were aware of the positive power void coefficient, so they added safety systems to prevent reactor operation in bad regions. On the night of the accident, a maintenance shutdown was scheduled but on scram the operators wanted to run a turbine spin down test, i.e. after the scram, see how long the residual steam could drive the turbines before backup systems had to be operational. Previous attempts to run these tests had failed and the operators were pressured by Moscow to get it done or else (Siberia?). To maximize the chance of a successful test the operators maneuvered the reactor into the low core flow, low power region of the reactor's operating domain with the dangerous positive void coefficient and thus positive power feedback. To get the reactor into this state the operators had to override numerous safety systems designed to prevent such operation. At the commencement of the test there was a power excursion that led to a power runaway that cause a steam (not a nuclear) explosion that blew the lid off the reactor.

One final important point, the Chernobyl reactors (and all RBMKs) are not housed in any containment structure like Western reactors (they are too big). The containment buildings of reactors like TMI or Fukushima are designed to withstand and contain the operating energy and nuclear material should anything go wrong and as these accidents have shown, they work. The Chernobyl accident was made much worse because the lack of containment allowed widespread dispersion of radioactive material due to the explosion and subsequent graphite fire.