Conflation: To Blend or Confuse (Perhaps with the Purpose of Misleading Someone)

There's inflation (to get bigger) and conflation (to bring together). You may have heard people say something like "she's muddying the waters," evoking the idea of someone stirring up the dirt so you can't tell where the water begins and the dirt ends. Or two rivers coming together like the mighty Rio Solimoes (the Amazon) and the Rio Negro.

In arguments, conflation is used when you try to point out to your opponent (or audience) that the thinker is taking one thing and confusing it or muddling it up with another. An example might be something like:

Hitler was a terrible person. He was really immoral.

Hitler believed that the world was round.

The world can't be round, because Hitler was immoral.

Oops, you're conflating Hitler's moral character (or lack thereof), with a statement of truth or falsehood; whether the world is flat or not. We're conflating two separate logical concepts. The world either is, or is not flat, independent of Hitler's moral character.

Wikipedia has a fun, image-based example of conflation from Biblical literature:

An illustrative conflation brings together two Roman Catholic saints named Lazarus. One, a lame beggar covered with sores which dogs are licking, appears in the New Testament (Luke 16:19–31).[6] The other, Lazarus of Bethany, is identified as the man whom Jesus raised from the dead (John 11:41–44).[7] The beggar's Feast Day is June 21, and Lazarus of Bethany's day is December 17.[8] However, both saints are depicted with crutches; and the blessing of dogs, associated with the beggar saint, usually takes place on December 17, the date associated with the resurrected Lazarus. The two characters' identities have become conflated in most cultural contexts, including the iconography of both saints.