.38 Specials work in the .357 same as .44 Specials may be fired in the .44 Magnum. In each instance the longer Magnum case was designed simply by lengthening the Special case. The longer case prevents accidentally chambering a Magnum in a Special, but does not prevent the reverse. There is no reason to prevent the reverse, as the Specials are all lower pressure than their Magnum counterparts.

The only drawback to shooting Specials in Magnums is lead bullets will gradually build up a ring of lead in the extra space the longer Magnum cases otherwise occupy. That can prevent chambering a Magnum cartridge or can make it very snug. You should not fire the Magnum cartridge in that instance, until you clean the deposit out of the cylinder. It can raise pressure substantially if you don't clean first, because the snug constriction prevents the case mouth from letting go of the bullet normally.

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Nick

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CMP Certified GSM Master Instructor
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"First contemplation of the problems of Interior Ballistics gives the impression that they should yield rather easily to relatively simple methods of analysis. Further study shows the subject to be of almost unbelievable complexity." Homer Powley