The transfer can be within the same financial institution or to a different financial institution and is functionally the same in that the funds are moved directly from one account to another without any payment of funds to you personally.
It's not uncommon for bank personnel to mistakenly believe that any movement of funds out of a particular IRA account is a distribution, so you want to be wary of anything that suggests that the movement of funds involves a reportable distribution. Every time dealt with an inherited IRA held by a bank custodian I've had to educate them on the difference so that they would not mistakenly report a distribution. (Many banks use standardized forms provided by the firm Ascensus. These forms have separate boxes for transfers and for distributions. If this is the form that is used, make sure that it is marked to indicate a transfer, not distribution. bank personnel tend to have a bad habit of always marking the distribution box.)
