Competition between companies use several forms of strategy to corner the market.
Not sure what exactly you mean: Doesn't production include a cost component? Wouldn't it be more important to ask on specific outcomes you want to compete with, e.g. high quality manufacturing or cost efficient production or a combination of several factors?
From a strictly microeconomic point of view, there is no difference since one is the dual of the other: you can minimize costs or maximize production, but the profit equilibrium is the same.
If you are interested in strategies to compete you may want to look into some of the "classic" literature, e.g. from Michael Porter.
Try to specify your question for yourself: “strategy on costs” – can have different focuses, like cost minimization per single product (by given demand e.g. per anno) or cost balance in the production (non-conformance against quality-control-cost) etc. “strategy on production” could mean max production with given resources (time, men, machine etc.) or flexibility of delivery (time, demand) or stability of production processes (0 mistakes or robust (mistake tolerant) processes) etc. There is a lot of literature to each of these directions, but there is no functional concept so far, that shows you all these directions in an optimization system. In the iterative process of specifying your question, you should be able to answer it yourself.
Of course there are differences in the two strategies. I also understand that it has to do with the market or markets to which it is addressed.
You can have high costs and produce on request outside your organization. Or you can have low costs and high production series.
The correct strategy should be one that allows to reach that market and at least break even. Maybe in the overall portfolio, the organization has increased profits, depending on the market or segmentation.
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