Never heard of a motorcross bike.
Offroad is a bike typically made for more technical, tight trails, or desert (wide open and fast) riding. Some with a headlight, some without.
Never head of a deulpurpos.
by dual puprpose he might mean enduro or dualsport. Trail bikes are usually 4 strokes althought now I dont know wtf would classify as a trail bike. 2 strokes used to be your race bike but now 4 strokes are. and dualsports are usually 4stroke dirtbikes with a headlight tail light signal lights and some mirrors.
I think Okie was just trying to poke fun at the horrible spelling. Im sure he knows what bigtim meant, but like most of us is not going to waste the time answering the question if the guy cant be bothered with making the post legible. Or I could be totaly wrong in which case I will crawl back under my rock... :whoa:
Let me take a stab based on some head scratching and wild guessing.
MX (MOTOcross) could be 2 or 4 stroke is in it's element on a closed track, may meet minimal sound but no spark arresting or lighting features.
Offroad aka desert aka hare scramble aka trail bike aka enduro etc... could be 2 or 4 stroke typically must meet USFS or other governing agency standards for sound and spark arresting exhaust. May or may not have lights.
DS (dual sport) a bike that can legally be ridden on public roads, is registered in the state the owner lives just like a car. Tires must be DOT and other standards as required by each state.
Can you use a MX bike on trails? Sure. Can you use a trail bike on the track? Sure. Can you use a dual sport for the other uses? Sure. But a DS is not going to be stellar at any one thing, a trail bike will be better for putting around on trails than a full on MX for most folks even though most folks seem to think they need a full one MX bike for typical off road use. Bottom line you will be happiest if you are honest with yourself about what the bike will REALLY be used for and what your skill level REALLY is or will be in the reasonable future and then getting a bike to suit those parameters.