Rakesh,
Basic differences are as follows;-
ASME I - Concerns power / fossil fuel fired steam boilers / ASME "V" Stamp
Safety Valve design requires full opening @ 3 % overpressure, blowdown (closing) at 2 to 4 % (below set pressure), Testing on steam at manufacturer (unless dispensation obtained).Lever mandatory.
Typical designs are open bonnet, nozzle and guide ring, butt weld or inlet flange.
ASME VIII - Concerns process equipment (all fluids) / ASME "UV" Stamp
Safety relief valve design requires full opening at 10 %, demonstrated blowdown of typically 7 % (during capacity test) for compressible fluids. Mandatory lever for steam and water above 140'F. Testing or air/nitogen, water and/or steam at factory.
Typical designs have single nozzle ring, flanged connections (per API-526), although threaded thermal relief valves can be covered by ASME VIII.
Also, pilot operated valves covered by both codes.
In your case existing ASME I safety valve most probably can cover the ASME VIII requalification, but vendor will have to confirm as sizing is affected by nature of overpressure difference (should be OK since required orifice area would be larger if no other conditions change). Valve would not meet API-526 but this is not mandatory.
Installation in European Union would require PED/CE compatability check by vendor.
Per ISO, only the term Safety Valve is used for all overpressure eventualities regardless of design.