In academic literature, "statistical arbitrage" is opposed to (deterministic) arbitrage. In deterministic arbitrage, a sure profit can be obtained from being long some securities and short others. In statistical arbitrage, there is a statistical mispricing of one or more assets based on the expected value of these assets. In other words, statistical arbitrage conjectures statistical mispricings of price relationships that are true in expectation, in the long run when repeating a trading strategy.
Global macro is an investment strategy based on the interpretation and prediction of large-scale events related to national economies, history, and international relations. The strategy typically employs forecasts and analysis of interest rate trends, international trade and payments, political changes, government policies, inter-government relations, and other broad systemic factors.
This is from wikipedia. From my personal (although I am likely incorrect) experience, stat-arb involves development of regression models using various factors to value an asset and determine relationships in asset prices and macro/fundamental data. If the difference is significant enough that the expected return on a trade "betting" on a reversion to the models estimate, a profit can be incurred. Thus the trader allocates their portfolio according to expected risk adjusted returns.
In quantitative macro trading, economic trends are forecasted and positions made accordingly. By this approach, it seems a model is still necessary to translate economic expectations into asset price trends. Thus it seems all quant macro traders are stat-arb traders. They are just using expected data for model inputs rather than current data.
Is my assumption incorrect?