Bear, produce, yield, turn out are comparable when they mean to bring forth as products.
Bear usually implies a giving birth to offspring or a bringing of fruit to maturity, though it may be extended to something which tends to reproduce itself or to aid reproduction.
Produce is far wider in its range of application, for it, unlike bear, carries no clear implication of a carrying during a period of development prior to the bringing forth; it may be used of almost any bringing forth or into view whether by human or natural agency.
It may apply more specifically to the bringing forth of something as issue of one's body, one's mind, or one's imagination or as an output of labor or effort.
Yield (see also RELINQUISH, YIELD) fundamentally implies a giving out (as of something within the confines of a thing or within one's power of production); it therefore stresses the outcome, result, return, or reward and not the previous effort or endurance.
Turn out, like yield, stresses the outcome or result, but it implies previous and especially mechanical labor or effort.