Hard cap is the maximum amount a crowd sale will receive or the maximum amount an ICO will be raising. If the ICO reached its hard cap, thy will cease to collect more funds. Soft cap on the other hand, is the minimum amount the ICO needs to raise, or minimal amount required for the ICO. If the ICO is not able to raise the said amount, the project may be cancelled and the funds are then returned to its investors.
Yes, you definition is right, but I have seen some flexible hard cap like the one Bancor team used to rake money from their investors, allowing the ICO to run for more hours even after the hard cap has been raised, just understand in full what the team is sayig and what their intention is truly is