To make it easy: Forests are in the North (USA, Europe). Animals that live there deer, rabbits, foxes, etc. Jungles are humid and tropical (Africa, Asia, South-America). Iconic jungle animals are tigers, monkeys and snakes.

The biggest difference is that most temperate forests lose their leaves in winter. Jungles lose their leaves all year round. On the ground jungles and forests are pretty similar - depending on the trees etc. There's lots of shade, clearings, leaf mulch and dead trees and branches.

Neither word has a very precise definition. I think a forest is called a "jungle" if it's in the tropics and it doesn't happen to be called a "rainforest." Similarly, a hurricane is called a "typhoon" if it's in the western Pacific. I don't think you can say much more than that. Scientists don't seem to use the word "jungle," but simply speak of different kinds of "forest," by latitude and tree composition; thus, "tropical forests" include "evergreen rainforest," "seasonal rainforest," "semievergreen forest," "moist deciduous forest," "dry deciduous forest," etc.