Single pulse is just that, a single pulse. Enough time is spent between pulses that there's no evidence of the prior pulse. Namely that TJ returns to the 25°C specified in the conditions. This may be a duty cycle much less than 0.1%.
Power dissipation is DC -- and at that, they don't often say so but this may be performed literally with the whole case at 25°C. This is achieved by immersing the part in a pool of boiling, nucleated* Freon. The full latent heat of the coolant is available to bring every point on the component surface to the rated temperature, even under extreme heat fluxes.
*That is, full of fine bubbles ready to expand into vapor.
It's not clear how often this technique is used. I recall an appnote back in the day which basically amounted to, "yeah we know this method is specsmanship and hopelessly unrealistic, but, they [competitors] do it, so we do it too". Or maybe it was actually AN-1140 and I've forgotten the context of the original document, or the surrounding conversation, from that long ago.
In any case, it's a shame that datasheets never discuss it, and appnotes rarely do. Presumably there are semiconductor standards set for it (by SEMI, JEDEC or other groups), but they are obscure, and not readily available or leaked online. Or even if they are, not knowing exact keywords to search for, they don't turn up on modern search engines which prioritize other kinds of material. In short, unless you're in the business, these standards are just about nonexistent.
Two which do mention the method are:
Application Note AN-1140, Continuous dc Current Ratings of International Rectifier’s Large Semiconductor Packages (International Rectifier), and
Semiconductor and IC Package Thermal Metrics (SPRA953C) (Texas Instruments).
These also seem to suggest the modern method is to use a fluid-chilled cold plate -- on the heatsink surface proper, not all over. A more realistic condition, representative of standard and recommended heatsinking practice.
In any case, the temp rise between junction and case, or case and heatsink and ambient, needs to keep TJ within limit. Simply add up the thermal resistances, multiply by power, and there is your temp rise.
There may be additional limitations, which AN-1140 goes into detail of. If bondwire, lead or package limits are specified, they must also be respected, and the die limit is essentially irrelevant and can be ignored. Note that any current limits are simply power limits, converted by element resistances. You don't need to know the wirebond diameter and material, or resistance, just its current limit.
And to be clear, what matters for this spec is average power, i.e. continuous, DC, over a long period of time. For pulsed operation, it averages out somewhat, and this is described by the transient thermal response plot (usually found in the datasheet). Data are given for continuous-pulsed operation (at given duty cycles, square pulses) and single (being by the same condition as before: TJ(initial) = 25°C or whatever).
It is perfectly reasonable for the chip to dissipate extreme amounts of power, for tiny fractions of a second; as long as TJ is respected even instantaneously (say, within ~µs), and then over time (ms to s), the heat eventually spreads out into the package and heatsink.
- Duty cycle can be calculated, or at least estimated, from the thermal impedance plots. Further reading: Power MOSFET Thermal Design and Attachment of a Thermal Fin (Toshiba)
Regarding the 800VA inverter, it uses class D operation. They simply never dissipate anywhere near 800W, at least for more than a fraction of a microsecond. The load line swings very rapidly between low voltage at high current, and high voltage at low current. Both extremes have little dissipation, and very little time is spent in the high-dissipation region inbetween.
That said, it's not clear what you intend to accomplish with your 70V 400A 10µs pulse, if anything at all. If these are the supply voltage and load currents, and you intend to operate in a switched mode, you are apparently ignorant of the above option. Perhaps you're making a fast electronic load or something, and the device dissipation is the point, I don't know. If you intend to build something like an inverter, this does not bode well for your success, and much learning is suggested before attempting a full scale (100s of W) design.