The required thickness is the minimum that is allowed as per the calculations according to the applicable design code.
Because this required thickness generally does not correlate to a commercially available/standard product size - the next thickest/largest size is usually choosen. This thicker wall is then the actual thickness.
For example, let's say (for a vessel made of 10" pipe) that after going through the calculations that you find a required (minimum) thickness of 0.425" - the next readily/commercially available wall thickness is 0.500" (XS); you would then purchase this 0.500" wall [allowing for undertolerance as well, but that is a separate issue]. Hence: required thickness = 0.425" & actual thickness = 0.500"
For further discussion, including MAWP and Design Pressure - please see this thread:
Actual thickness has been determined by measuring (e.g. ultrasonic thickness testing) already inservice equipment. In which case, if this measured actual thickness is lower than the required by calculation thickness - you have a problem.
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<...Actual thickness...> is greater or equal to <...Required thickness...>, otherwise the equipment will not pass burst/collapse insurance inspection and testing.
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Vessel design
Re: Vessel design
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