- Am I interpreting the results correctly?
- Do I interpret the results correctly?
Do they have the same meaning? Are both or just one correct?
Certainly either is correct, and they are equivalent in meaning. You're much more likely to hear #1, though. You might hear #2 in a confrontational context.
If both of those sentences were coming from a native English speaker, then I'd say that they don't convey the same meanings.
#1 is seeking confirmation that the speaker's interpretation of the results up to this point in time has been correct.
#2 sounds a little strange in this context, but is asking for clarification as to whether the speaker should, as a future action, interpret the results correctly (as opposed to, say, deliberately producing an inaccurate interpretation).
A more natural usage of the construction from #2 might be, for example, if someone is asking for directions: "Do I go left or right?"
Coming from a non-native English speaker, I might interpret #2 as meaning the same as #1, on the grounds that some languages don't distinguish between the present continuous (#1) and the simple present (#2) in the same way as English, so it may be difficult for the speaker to know which form is appropriate in cases like this.
I think #2 is valid and equivalent to #1, but #2 is less common, not only because English is prone to using the present progressive where other languages would use simple present, but also because #2 is somewhat archaic and sounds more formal. Another common construction with basically the same meaning would be "have I interpreted these results correctly?"
For #2, consider a person making a statement about what they've just heard, followed by "do I understand you correctly?" All of these phrases have the same meaning in context: seeking affirmation.