I received a couple of master's awards from my supervisor's grant and a graduate scholarship. Do those count as an academic honor or not?
If I understand correctly what you mean, I would argue that no. You should only list awards that are competitive (only a few students get them), are merit based (so not just given on a first-come-first-serve basis), and not automatically granted based on another achievement.
I'd imagine that you had already listed your master's degree on your CV, and mentioned your supervisor. Getting a graduate scholarship is not an 'honor' beyond the honor of being accepted to the graduate program (unless most students aren't supported); similarly, if you have a thesis advisor supporting you, you did not really compete for the award.
The same rule holds for conference travel grants. In my discipline, these are awarded at random, unless you are a best paper award recipient. If your paper was accepted to a conference then there's no point listing that you got some partial funding to go there. Again, you get that award because your paper got in + randomness, or because your paper was the best, in which case the travel grant is automatic (not an award in itself).
An award would be winning some prize (best paper, best poster, best presentation etc.); getting some competitive grant/scholarship (like a Google or Facebook fellowship); or an academic achievement (dean's list, valedictorian etc.). If you got accepted into a highly competitive program during your studies that might also qualify (say, you won an industrial internship at some company for outstanding academic performance).
My personal impression is that many students tend to inflate this part of their application. They list things that aren't honors (e.g. completing an online course certification), or very minor ones (e.g. 3rd place in a local high-school competition). This makes no sense to me. It makes it harder to distinguish the noise from the signal on student's current quality, and actually makes me generally more adversarial towards these applicants.
Good luck with your application