When did the US Dollar change?

You are correct - It has everything to do with the Gold Standard.

Up until 1933, all US Federal Reserve Notes were redeemable in gold coins, which were still being made for circulation. When the US dropped the gold standard and minting of gold coins stopped, the Series 1934 Federal Reserve notes had to be issued with the "Redeemable in Gold" clause removed. In fact, that is the major difference between Series 1928 and Series 1934 Federal Reserve Notes.

By the way, "IN GOD WE TRUST" wasn't added until 1957.

All the "paper money" currency was in a transition period from the old large size notes to the present day sized notes. Also some of the notes had different colored inks and uses. Some were silver certificates, others for gold. Eventually as the funds for various metals have decreased, or the prices of the metals increased to be worth more than the currency the Notes had to be changed to reflect the change. Currently we only use federal Reserve Notes. And all those notes have all the same wording. Also note the reverse "backside" of the note, it does not say "In God We Trust".