almost
thats not totally true.
a motocross bike is set up with the minimal equipment. up until recently they were mostly 2 stroke but yz450, cr450 and the like all 4 stroke, they race with 250 two strokes. motocross bikes generally have more suspension travel, are lighter and are all kick start. Off road bikes can be two or four stroke. yamahas off road bike is the wr(now the 450 but for years was 250 two stroke only) they also have other lines, ttrs and so on, suzuki for years had the rmx250 two stroke and so on. off road bikes usually have a wider transmission ratio(yz450 is 4 speed, wr is 5 speed) and they are usually geared and tuned for more midrange and low end power. enduros are on and off road which would be your klr models in kawasaki. they are all 4 stroke in the states here because of emissions laws but thats not true if you go back far enough. I used to have an 81 ke125 two stroke enduro.
there are tons of small differences but really you should choose a bike that suits the type of riding you want to do. If you are new to riding and you want to do mostly off roading and not really jumping or racing you should look into a 4 stroke, they are much easier to learn on and less intimidating in terms of power.