You do not need any new dies. You simply properly adjust those dies for the case length of the caliber you are reloading.
HOWEVER - if those old dies are not carbide dies, I strongly recommend that you do throw them away and buy new .38 Spl dies. While steel dies will work just fine for both .38 and .357, the trouble of messing with case lube just ain't worth the small cost of a new set of carbide dies! (Actually, the only new die you need is the sizing die - so if you can buy just a carbide sizer - ANY brand - cheaper than a new 3-die set - that is the way to go. Personally, I'd check out a Lee carbide sizer for .38 Spl.)