Well there might be different wording where you're from, i have heard the use of demi before.
I got taught that a temporary haircolour is something like wella perfecton rinse, or coloured sprays or chalking that wash out in 1-2 washes.
A semi is a non oxidising colour such as wella colour fresh, directions, crazy colour etc that you apply straight from the tube and it lasts 2-10 washes, more or less depending on condition of hair, porosity, styling (cos hairspray strips semis right out), how often you wash and what shampoo you use.
Quasi is mixed with low levels of peroxide, so wella colourtouch, infiniti satin etc and it is usually used to tone or same depth/darker colouring, blending in early greys etc, and this fades out as well as growing out.