Tube has an OD, so 1" TUBE has an outer diameter of 1" (inside diameter of 1"x1/8" wall tube would be, 3/4")
Pipe has an ID, so 1" pipe would have an INNER diameter of 1".... you would think exactly one inch, but pipe (the black stuff you get at home depot and what not) really has an ID that is variable and bigger than 1" so you will get wiggle room, sometimes a lot of wiggle room.
Most precise measurements are done with DOM pipe or tubing, they are just more precise and can be purchased usually for less $$ from your (google 'steel distributers near me') hardware store. (e.g. home depot would sell a tube for $10, when you could get it for $2 at a steel supplier. Also, why not do like two steering stem bearings like they do with motorcycles? It will make for easier turning/last long.