You wrote "HIPS", where I am used to the term HIPPS, being High Integrity Pressure Protection System (see for example NORSOK standard P-001).
A HIPPS is a Safety Instrumented Function (SIF), provided to protect against overpressuring and with a high integrity (so with a low probability of failure on demand/a high Safety Integrity Level (I would say SIL3).
As described in the IEC 61511-1, a Safety Instrumented System is an instrumented system used to implement one or more Safety Instrumented Functions.
So in short, a HIPPS is just another word for a SIF with SIL 3 to prevent exceeding of design pressure. The term HIPPS was probably invented before IEC 61508/61511 and terms like SIS, SIF and SIL were invented.