It depends on what the server supports. So:
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The tags don’t sync. That means if you tag a message on one device, on the other device it has no tag.
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The tags on messages do sync. That means if you tag the message on one device, you see the same tag on the message on another device.
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The tags on messages and the list of tags sync. That means you see the tags on the messages on the other device, and if you go to Menu > Tags, you see the list of server tags for that account as well. So if you create a new tag on one device, even if you don’t use it, you will see it in the list on the other device. That is for server tags only, as the list of Local Tags doesn’t sync.