The difference between Engender and Produce

Engender as a verb (obsolete, transitive):

To beget (of a man); to bear or conceive (of a woman).

Engender as a verb (transitive):

To give existence to, to produce (living creatures).

Engender as a verb (transitive):

To bring into existence (a situation, quality, result etc.); to give rise to, cause, create.

Engender as a verb (intransitive):

To assume form; to come into existence; to be caused or produced.

Engender as a verb (obsolete, intransitive):

To copulate, to have sex.

Engender as a verb (critical theory):

To endow with gender; to create gender or enhance the importance of gender.

Produce as a verb (transitive):

To yield, make or manufacture; to generate.

Produce as a verb (transitive):

To make (a thing) available to a person, an authority, etc.; to provide for inspection.

Produce as a verb (transitive, media):

To sponsor and present (a motion picture, etc) to an audience or to the public.

Produce as a verb (mathematics):

To extend an area, or lengthen a line.

Produce as a verb (obsolete):

To draw out; to extend; to lengthen or prolong.

Produce as a verb (music):

To alter using technology, as opposed to simply performing.

Produce as a noun:

That which is produced.

Produce as a noun:

Harvested agricultural goods collectively, especially vegetables and fruit, but possibly including eggs, dairy products and meat; the saleable food products of farms.

Produce as a noun:

Offspring.

Produce as a noun (Australia):

Livestock and pet food supplies.