The jet in the first of the video is a British Nimrod, the military version of the Comet which gained such a bad reputation in it's early years--for literally coming apart at the seams because of pressurization problems
The one you speak of with the smoky startup is a form of the Canberra, which uses a form of Coffman starter cartridges, just like famously shown in the original version of "Flight of the Phoenix" The object of these was that if you were "somewhere" you could start the engines with little ground support, no need of a big auxiliary compressor/ generator/ etc on wheels
An explanation
http://www.pprune.org/aviation-history-nostalgia/380056-coffman-starter.html
and........
http://en.wikipedia.org/wiki/Coffman_engine_starter
[ame="http://www.youtube.com/watch?v=g9fkmqPHTDE"]Canberra cartridge start Brunt 2009 - YouTube[/ame]
[ame="http://www.youtube.com/watch?v=AwYzAF9bZLI"]Flight of the Phoenix Starting the radial engine with Coffman cartridges - YouTube[/ame]
The real thing:
[ame="http://www.youtube.com/watch?v=65qrzgbTTcQ"]Wildcat First Shotgun Start - YouTube[/ame]
Go to about the 57 sec. mark.............
[ame="http://www.youtube.com/watch?v=Os19XiWGDjs"]Grumman F3F-2 "Flying Barrel" - YouTube[/ame]
And let's not leave out the German? "Field Marshall" traktor which I believe is somewhat different. The thing they are lighting is sort of a fuse/ glow plug. These are not true diesels, rather "hot bulb" engines, more like a "glow plug" small model engine, and will burn about anything that is oil and will burn
[ame="http://www.youtube.com/watch?v=01Sr8S9uQMc"]how to start a field marshall with a shotgun cartridge - YouTube[/ame]