No. The same convention is followed by both. There is nothing special in the linkage rules for a subroutine that calls itself.

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stack frame Local variables and stack frames.
stack frame, picture Picture of a stack frame.
frame pointer, reason for Reason for having a frame pointer.
variable, as displacement into the stack How local variables are used in assembly language.
frame-based linkage convention Our frame-based calling convention.
storage classes Storage classes: automatic, static, dynamic.
entry point Entry point.
recursive call Recursion