In biology, an offspring was the product of reproduction from one or more parents. Offspring were an integral component to building a family, where they may be identified one's son (a male offspring) or daughter (a female offspring).
Some species did not rely on offspring as a means of continuing the species. For example, the J'naii and the Changelings were two species that reproduced in other ways. (TNG: "The Outcast"; DS9: "The Search, Part II") Prior to the intervention of the USS Enterprise on Gamma Trianguli VI, the planet's inhabitants had no need for what they described as "replacements", as they were forbidden by Vaal. (TOS: "The Apple")
The term child (plural: children) was referred to offspring, specifically that of humanoids, while childhood, in essence, follows the stages of child development from infancy to adolescence. While the term generally applied to adolescents, the term "child" could continue to apply to adult members of a species. James T. Kirk once described children as "little ones like yourselves. They grow." (TOS: "The Apple") A biological child was the term for a child produced biologically rather than artificially. (TNG: "Inheritance")
Richard Daystrom compared the M-5 multitronic unit he had designed to a child, developmentally. Dr. Leonard McCoy didn't care for the comparison but used it all the same when analyzing the scientist's mindset. (TOS: "The Ultimate Computer")
Occasionally, beings posed as a child to gain insight into Humanity's existence, strengths, and weaknesses. (TNG: "The Child", "Imaginary Friend") The children of Drayan II were individuals nearing the end of their lives, rather than beginning them. (VOY: "Innocence")
In 2373, multiple children were seen in a mind meld which Tuvok and Kathryn Janeway participated in. One of the children, a young girl who was desperately clinging onto each of the other children's hands on the edge of a precipice, was actually a manifestation of a memory virus. The children who were holding onto her hand were Tuvok, Janeway, Dimitri Valtane, and multiple illusory children. (VOY: "Flashback")