Do they mean the same? Example sentence:
Her eyes were glazed. Was she about to cry?
Her eyes were glassy. Was she about to cry?
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To a first approximation, they mean the same. In fact, I would say the biggest difference is that syntactically, we're much more likely to use adjectival glassy-eyed and adverbial [with] glazed eyes.
But sometimes, some people will distinguish glassy-eyed as more evocative of an intoxicated state or similar (drunk, drugged, in extreme shock), whereas glazed eyes tends rather to suggest inattentiveness (through boredom or lack of comprehension).
having eyes that are void of expression, life, or warmth, esp because of drugs or alcohol
If you describe someone's eyes as glazed, you mean that their expression is dull or dreamy, usually because they are tired or are having difficulty concentrating on something.
Synonyms: expressionless, cold, fixed, empty
(I've highlight "void of expression" and "expressionless" to reinforce my point that there's a lot of overlap.)