Both are correct in American writing. First off, you need to learn how to form a question in English. "Do both mean the same?" Once you learn that so you never make a mistake, then you can experiment with colloquial language. We might say informally, "Both mean the same?" but usually only in speech, never in writing. But since "both" means "two" and two of something is plural, you have to use the plural form of the verb: mean, not means. Back to the question... Your use of "discretion" is simply wrong. I suppose the listener/reader would correctly figure out what you are trying to say, but we never use "discretion" in that way. Discretion is much more than judgment. I'm not going to go into the definitions here; please spend more time in your dictionary! If you don't have a good one, please become more familiar with Dictionary.com.