It may vary from hospital to hospital and also depend on how busy they are at the time. With first baby, you can still have a LONG time to go to get from 3cm to 10cm, so if you coping OK with the pain, they may offer the choice to go home & come back later - especially if they don't have any beds free in the labour ward. I went in three times altogether and was 3cms the first time I went in - 8 hours later when I went back I was still only 3.5cms
. To give you an idea my contractions first started on a Thursday night, I called my Midwife on Friday morning and she came to my house to assess me, told me I was doing nicely and to get lots of rest. They came on and off throughout Friday, then came on strong and frequent again Friday night. I eventually went into hospital on the Saturday morning as I realised my waters must have broken in the night (contrary to popular belief it isn't always obvious!!) and I didn't finally give birth until the Monday morning!! And apparently it's not that uncommon for labour to span over several days when it's baby no. 1.
They left it up to me though - so I think I could have stayed if I wanted to, or if I wanted pain relief, but it's soooooo much more relaxed and comfortable in your own home.
Re. distinguishing 'contractions' from normal pains, in my case it was VERY apparent as the contractions were pretty painful and I had to concentrate on relaxing. Also they are evenly spaced but get longer in duration and become more frequent over time. I asked the Midwife how you knew contractions from strong braxton hicks and she said with BHs you focus on the tightening of the uterus and it can be quite uncomfortable, whereas with contractions your first focus is on the pain - not that the pain is too bad, it's just that you notice the discomfort before the tightening.
Everyone is sooo different unfortunately - I know someone who experienced no pain, but her MW did an examination and found she was 3cms dilated and had probably been in slow labour for some time without even realising!! Also a friend I met at NCT had her baby (first one) in about 4 hours and didn't even use gas & air!
Your body gives you big clues and in my case I definitely knew things were happening - apart from having a show, I just 'felt' different on the day I went into labour.
Hope this helps (and doesn't freak you out - it's not meant to!)
Lots of luck & love
LBxx