So if you see something like a star at night moving, what could it be?

"It can't be any kind of space object."

Does that mean it must be a non-space object?

It's most likely a satellite.  If it moves roughly west-east it's most likely a civilian and/or scientific satellite.  But if it moves in a polar orbit (north-south) it's probably a military/spy bird.

Most likely a satellite of some kind. I've seen tons of 'em, like the ISS, the space shuttle, the old Mir, and quite a number of discarded rocket boosters.

Slow and STEADY----Most likely a Satellite. A quick flash a Meteor, Slow steady, blinking an aircraft.  Fast and steady, dim lit--a bird.  Garden Variety "UFO"  Fast with obvious, QUICK direction changes and a "slight "Skipping motion".----------There is NO evidence that a UFO is an "Alien spaceship"   we simply do not know WHAT it is---its the "U" for unidentified.

Depends on what rs speed and distance an aircraft is close so doesn't have to move fast to seem to move fast

Probably  the reflective surface of an orbital satellite.

the international space station

The ISS is easily spotted with the naked eye, With binoculars its shape can be made out

Any Sattelite will shine when  it has the Sun shining on it

If it is moving weirdly, then get your Cine Camera !!

God are the stars. God did not make them. If you saw one move you saw God moving. Most do not notice. I will look upon the earth from the Beginning of the year to the End of the year. 

any tds' are wrong.

Probably a satellite... they move at a fairly constant speed, have no blinking lights, and cross the sky in 3 to 6 minutes or so. You can usually see 3 or 4 inside an hour if you look hard on a clear night.