The Difference between Mail and Post
One's a bag, the other's a relay
The verb to mail, which came into American English1 in 1828, means to send by post. In the UK, people still post things, probably including mail which has been a noun for posted letters since around the year 1200. Mail meant a traveling sack, and eventually came to mean the kind of bag a post-carrier might employ. By the 1600s, the noun mail meant letters and packages sent by post, and the system of moving letters and packages by post, and people and equipment that carry letters and packages sent by post.
It's worth noting that the word mail meaning armor made of metal rings and the mail in blackmail are unrelated to the long-standing word mail you use to talk about letters and packages sent by post.
A post, of course, is a position. As early as 1500, riders and horses were posted a certain distance apart to provide a rapid relay for transmitting letters and packages. Between the 1590s and the 1660s, post took on many of the same meanings as mail, including the sense of a system or vehicle used to transmit letters and packages. In fact, because this kind of relay was so quick, post became both a verb and an adverb that meant go fast.2
As a newspaper name, post (1680s) predates mail (1789). Perhaps the daily post seems like the information has come faster, as it summons to mind the Pony Express, and perhaps the daily mail seems more comprehensive with all those letters and parcels.
The word post meaning mail is unrelated to post meaning a substantial upright pillar, but the word post meaning make known to the public means to affix a paper notice to a post (in the sense of pillar). When you post on Twitter or Facebook, you aren't riding electronic horses; you're nailing a notice to a screen. When you send an email,3 you're transmitting electronic letters and parcels (attachments). E-post seems like a missed opportunity, since email passes through many servers called relays, but there you go.
Seems like an oxymoron, but it ain't.
See post-haste.
An email is fine. Get off your electric pony.