TMP vs The Changeling (probe returns to earth )
This one is complicated, as the final version of TMP had such a convoluted evolution.
TMP also shares some similarities with Filmation's "One of Our Planets is Missing" and "Beyond the Farthest Star". Those eps have (Spock mind-melding with) a giant cloud and a giant alien vessel. The Marc Daniels and Samuel Peeples scripts for TAS were adapted into novelizations by Alan Dean Foster. Roddenberry was impressed with his work and asked ADF to distill a new story from an unfilmed Roddenberry story outline* for "Genesis II", "Robot's Return". That story was turned into a telemovie script, "In Thy Image", by Harold Livingston. Quite a few influences from Roddenberry's first attempt at a Trek movie, "The God-Thing", also crept in. Will Decker as son of Matt Decker, meant that the film had some thematic parallels to "The Doomsday Machine". TMP then started filming with a shooting script that was two-thirds TMP, with a slightly-altered final third lifted from "In Thy Image" (with Spock replacing Xon). As filming continued, the script was still being rewritten. As time ran out, Shatner and Nimoy even started suggesting endings to Wise and Livingston and the production seemingly began stealing more heavily from "The Changeling".
When I was at preview (and premiere) screenings of ST IV and, when it started, everyone yelled, "Not another probe!"
TFF vs The Way to Eden (religious cult leader takes over the enterprise )
ST V was very much Shatner's baby, but I think he really craved to have Roddenberry's approval and thought a "quest for God" theme - Roddenberry's own elusive theme for "The God-Thing" - would achieve that. Except that both Roddenberry and DC Fontana denounced Shatner's use of a Spock sibling (ie. Sybok). DC even brought out her file copies of memos she wrote during the TOS days as to why a Spock sibling was an idea to be avoided. "The Way to Eden" is not the only episode to mention "Paradise" (there was also "This Side of Paradise" and "The Paradise Syndrome" - and "Paradise Lost" was quoted in "Space Seed").
Parts of "Into Darkness" retell the story beats of "The Wrath of Khan".
* Corrected.
