The first implies that since price of an asset accurately reflects the (appropriately discounted) stream of earnings that it is expected to yield over the course of its existence), price signals can be relied upon to efficiently allocate resources among the various sectors within the financial markets. The second means that it is impossible to beat the market on a sustained basis by arbitraging on mispricings (and therefore passive index funds are more efficient investments than actively picking stocks).
Rajiv Sethi has an excellent post that draws the distinction between the allocative and informational efficiency dimensions of EMH, with the former corresponding to the strong and the latter to the weak forms of efficiency respectively, and argues that neither are states of efficiency. He writes,
"Prices may indeed contain "all relevant information" but this includes not just beliefs about earnings and discount rates, but also beliefs about "sentiment and emotion." These latter beliefs can change capriciously, and are notoriously difficult to track and predict. Prices therefore send messages that can be terribly garbled, and resource allocation decisions based on these prices can give rise to enormous (and avoidable) waste. Provided that major departures of prices from intrinsic values can be reliably identified, a case could be made for government intervention in affecting either the prices themselves, or at least the responses to the signals that they are sending. Under these conditions it makes little sense to say that markets are efficient, even if they are essentially unpredictable in the short run."
In view of the considerable range of non-fundamental information on market psychology that prices reflect, Rajiv Sethi prefers that EMH be renamed as the invincible markets hypothesis (IMH)!