It’s really hard to tell the difference, since many projects in attempt to bypass legal regulations for the ICO start to call their fundraising campaign crowd sale instead of ICO.
ICO can include pre-sale and public sale, during both phases project raises funds and emits tokens. On the other hand crowd sale is more like public sale phase.
By the way, there can also be pre-ICO, which is more about raising funds for project’s ICO and without token emission (but with some agreement). Pre-ICO is not Initial Coin Offering, because if it fails there won’t be any token emissions or transfers.