To me, in England, it means same bed. I co-slept with my baby or rather, 'we' (husband and I), did, with our baby between us once he got a bit older. We were careful and safe. When he was very tiny he slept in cot right next to my side so I could get him out easily when he woke for feeding and cuddles. It was nice!
This was years ago - and I mean 'years'. At that time co-sleeping was frowned upon, babies were 'put to bed' in their cots at a certain time (sometimes in their own room!), and expected to stay there except for night feeds in the first few weeks; we used to try not to let people know he slept with us. Even our parents said he should be in his own bed and once he was a few months old, in his room. They also thought he should be left to cry for a while and we were 'spoiling' him. After a while they gave up.
In later years I found out that lots of his friends, though not all, co-slept for years and I didn't feel so worried about it.
We didn't squash him, all three of us slept like logs and he is alive, well and kicking at 41.
Do what is right for you and your baby.