Hashtag is a way of organizing like "tweets" if someone uses them correctly. Think of a hashtag like a subject or folder in your email. Anyone that hashtags LVC in the format "#LVC" would "categorize" their tweet with others using hashtag LVC in the format "#LVC". These hashtags are all in one area if you were to search for them, I really haven't searched for hashtags, except to see if anyone else has used it since I come up with some odd hashtags. I really don't see a reason behind it except organizing like tweets in the Twitter world.
Likewise, a "Twitter Handle" is like a username in the format, @mlara1129, @LS4me, etc. It's like the "To:" or "Recipient" part of the email if you're tweeting to someone. They will directly receive the tweet and be able to read it, instead of hoping it would show up on their timeline which is like your inbox in email. The people you follow on Twitter, their tweets show up on your timeline. The people who "mention" or send you a tweet, have their tweets show up in a separate section of Twitter.
Obviously, I tried to relate Twitter to email since more people use that. Long story short, given people's access to the internet and smart phones, things done on Facebook, Twitter, etc. can all be accomplished in email if done right. At least from my point of view. The only difference is that most people don't check their email religiously but would check Facebook, Twitter, etc. every 5 minutes. At least with email, you're not publishing something to the www.
Social media, although I understand it, a lot of people abuse it. I'd rather be on LVC

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