in the 1920's和in the 1920s的用法都对吗,各自指的是什么年份

都对,意思是一样的
in the 1920's 比 in the 1920s 要更正规,前者是一种标准的说法,而后者并不正式,但是人们已经完全习惯这么使用了,所以现在大多数人,大多数文字都是说 in the 1920s
参考：
According to The St.Martin's Guide to Writing,5th Ed.,the correct way to form a plural of a number is to add an apostrophe and an "s." Therefore,1920's would be correct.