I view 'imply' as 'suggest' and 'prove' is 'this is a fact'. Correlation does in fact imply causation (which is why correlations are investigated). It just doesn't prove the causation. It may be that the two things you're looking at are both related to some other cause (e.g. ice cream sales and murders increase in summer, supposedly. This does not mean ice cream sales has a direct relation to murder but they probably both have a relation to outside tempature), it may even be pure coincidence. But if you see a correlation you see a place to begin your investigations.