What does Josiah mean?
From Hebrew Yoshiyahu, a theophoric name ending in Yah (Yahweh). Lexicons (BDB) read it 'Yah supports/supporteth'; the underlying verb (yasha) carries the sense 'save, deliver.' The popular rendering 'Yahweh heals' is common on name sites but is not supported by the root, so 'supports' is the better-attested gloss.
What does Seth mean?
From Hebrew Shet, tied to the verb shat, 'to set, place, appoint.' Genesis 4:25 explains it through Eve's words 'God has appointed (shat) for me another child' — a biblical wordplay that is consistent with the underlying root.