I wouldn't go as far to call the synonyms.The point is, in our society as a whole, they are pretty much synonymous. Even if you don't want it to be intimate, you still need to clear that with your chosen partner. No matter how liberal society becomes, it will never reach a point where no one prefers intimacy, therefore you will always have to check.
Below is quoted from Wikipedia, but you'll find similar defs in other places as well.
Genuine intimacy in human relationships requires dialogue, transparency, vulnerability and reciprocity.
How often do you think a man and a women dating several times then going to bed together will (the staus quo, mind you, you don't marry every women you sleep with , and a lot of women will also dump their partners ) meet the above factors ?
It's a very long process which does not take place in days or in weeks. It seems to me that sex or "physical intimacy" to use a widely popular term is far far from intimacy in close social relation.
How can a person in his/her right mind expect intimacy with someone you have barely know since 2 weeks ago. With all good intentions, all I could expect is that this is a possible relation with the potential to go well and reach after one year or more the status of intimacy.
So why would you check ? If someone is willing to sleep with you after the initial few dates, you can assume that she see the same thing, the potential for a relation, and nothing more. No one should expect that the women to be so stupid to empty your heart in front of you, share with you her darkest secrets and become totally vulnerable.
So then how the heck can sex be "the most intimate thing youll ever do" ? For me personally the most intimate thing I could ever do is to become vulnerable.