Retirement tax questions

I shall be  72 by the end of October 2022.  I believe my 1st RMD must be  taken before April 1, 2023 and the 2nd RMD before 12/31/2024 correct? 

If my 1st RMD was taken on between 1/1/2023 to 4/1/ 2023.    Since I turn 72 in 2022, is that RMD taken in 2023 goes to TAX Year 2022 0r 2023?