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Characters with a notable difference in their voice get something to note that. In both DC and Marvel, although I've seen more instance in Marvel.
Thor's font typically has an "olden" style to it. It wasn't always like that though, I have no idea when it was introduced.
Sometimes Beta Ray Bill get a unique font too.
Deadpool's got them either because he has the internal voice or because it's all fucked up and sounds like "gravel and gasoline"
Ultron gets the rectangular speech bubbles.
Skrulls get green, unless they are transformed.
Deathurge's speech bubbles are black with white font.
In some CosmicMarvel, aliens are given something notable to show they are talking in their alien tongue but it's just translated for us.
Nobody ever really says what these changes mean. So unless it's something obvious, then it just means they speak with an extremely clear difference to everyone else.