Telegram doesn't have an additional status for message delivered to device, because you can use our apps on multiple devices at once. Since you don't know which one of their devices the person is actually using, delivery to one of the devices becomes irrelevant.
1 check = message delivered to the Telegram cloud (and is waiting for your chat partner to see it in Telegram), notification sent (if the recipient has notifications turned on).
2 checks = message read (recipient opened Telegram and the conversation with your message).
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