Not sure about automotive parts but with standard parts (non mil) the biggest difference is the operating temperature.

Depends on the level of militariness.

The lowest level is simply mil temperature range

MIL-STD-883 also includes visual inspections and some degree of confidence about life test capability

SMD (Standard Military Drawing) is more rigorously qualified for military environments.

TTFN

Buzzp,
Yes there is a great difference in price and performance in electronic components either passive or active between automotive and aerospace.

While automotive may accept and use standard parts aerospace mostly uses custom parts. Also most parts use for aerospace projects are de-rated; Voltage de-rating and temperature de-rating. The de-rating is a safety factor, e.g. a 2200 micro farad capacitor 16V, may be used by an automotive company as a standard part for 16v application, but an aerospace may have to de-rated it by .25, hence use it for a 12V application. There are also a lot of other factors that come to play, such as the number and kind of test verification that may be needed to validate the specific component
Regards, Geke

I would question "most uses custom parts."  Since about 1980, the trend has been away from using custom parts in aerospace due to the cost and maintenance.  The customization in the current generation of military systems comes from the extensive use of commercially available FPGAs and other programmable devices.

I would likewise question the presumed lack of derating in automotive designs.  The operating environments of most automobiles ranges from approximately -20ºC to +65ºC.  The ability of all the processors and electronics to perform over this temperature range suggests very conservative designs with lots of design margin.

TTFN

I did not say anything about aerospace that I recall. Obviously, if the part is not in the pressured cabin then altitude plays a major role, especially with voltage. In any case, I did not mention aerospace but I understand the differences.
Many companies design their products to be used in environments well outside of the manufacturers specifications, especially with temperature. I do not agree with this at all. When you do this you are saying you know more than the mfg and just because it works one or ten times from a cold temp of say 50 below C, does not mean it will next time. I have seen this over and over again in the design world outside of automotive or aerospace (industrial).