wander = to move away from somewhere or to walk aimlessly. This is why parents say to children "don't wander off" indicates stay close to me, follow me for this context Roam = a little similar but means to travel without having a plan or a clear idea of where you are going or travelling to. This is way less often you will hear parents say "don't go roaming off" indicates don't go too far from me and go off somewhere without my permission. Stroll = to walk somewhere in a leisurely relaxed manner Ramble = to walk for pleasure usually in the country but it can be anywhere like along the coast etc. we usually say "I am going for a stroll" and "last time I saw him he was rambling/strolling through the forest" they are all interchangeable except for the child wandering off where we use a "set phrase" don't go 'wandering off' although you can say any of the others to a child and I have heard the others used to a child Edit P.S Ramble also means to talk a lot incoherently or just consistently non stop. Thank you to Michael