Cakes and/or barrages are exactly the same, it's just that different people call them different things...
They both consist of multiple tubes - different diameters & quantities for different sized fireworks, all glued together with a pyrotechnic fuse linked through each, and usually ending out of the top of the firework to appear as the 'the leader' fuse, which is what is ignited to start the firework.
As the fuse burns through the bottom of each tube it ignites a lift charge which in turn, (through a mix of fast-burning black powder and gasses) fires an effect into the sky which, after a pre-set amount of time, explodes to produce one or more effects of light and sound.

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