I absolutely agree they are different--that's really my point, that they function differently, and if they are changed to be able to function similarly, people will use them similarly and they'll lose their uniqueness. Namely, the text inbox will fall prey to the same issues that many email inboxes fall prey to, which is that they just get more and more filled up with messages that were already read, and messages begin to get lost.But Messages and emails are two different things organized by two different identification modes. You may think of them as two similar ways of communication but they aren’t. I would want to be able to archive my messages in the same way I do my emails but I definitely would not want the to merge. Your solution would just get messages lost in a sea of mails and be less organized, not more. I wouldn’t what my letters and phone calls treated the same, I don’t want my emails and messages treated the same either.
My suggestion of making it easy to forward specific texts to email inboxes wouldn't somehow get all the messages mixed up as you suggest. Text messages still remain in the text message app as always, but a copy of the text can be forwarded to your email inbox as a reminder to take action on it, just like your calendar sends email reminders of events. It would be obvious that it's a text reminder and not an actual email from that person because it would show the sender as "text reminder" or "text forward" or something like that, just like a Google Calendar email notification shows the sender as "Google Calendar". After action is taken, it can be deleted.