leak test only needs to be conducted with a fluid or gas or equivalent molecular size but may be an in-service test and at reduced pressures.
A hydro test is required per ASME code to confirm the structural integrity of the welds and bolting of the pressure vessel. Depending on the design code and the date of the design code used, various pressure multipliers are used.
If a recent design code is used and lower safety factors were used in assigning allowable stress , then a 1.3 multiplier on hydrotest ( using a liquid) is used. Odler codes that used a higher safety factor would require a 1.5 pressure multiplier if a liquid is used as the test medium. But please note: the minimum required hydrotest fluid temperature is EXTREMELY important- if you test at a metal tempature that is below the ductile brittle transition temperature, the vessel will fail catastrophically.
Similarly, some codes allow an alternate to the hydrotest- an air test can be done at 1.15 times design pressure, after conducting a leak test at a lower pressure . But such air tests have a much worse failure potential if conducted below the ductile brittle transition temperature, compared to a hydrotest.