They do have similarities
That said, these two realms of the internet weren't hugely different in the past. When you boil it all down they've both always just been ways for you to connect with your audience or market. With each method, you've got to ask yourself questions like these: What am I promoting or selling? Who am I pitching this content to? What will they be looking for? How do I get their attention so that I can be found by them? How do I impress them with my knowledge and expertise?
In the case of SEO, you're doing this through a massive computer called Google, so you have to be mindful of how it works and what it values.
Social media is human and immediate
When it comes to social media, you're connecting with people directly where they congregate and mingle online. So you have to work out what the characteristics of your target demographic are and find the social network(s) where they will be most concentrated. Once you've done that, you have to slowly get on their radar and build your authority by sharing quality, relevant content with them.
This is a more direct and immediate process than SEO, and that's one of the main reasons I prefer it. You can really get out there and be proactive about it. With every bit of content you share and every new person you follow and interact with you are increasing your footprint on these social sites. Before too long you will surely reach a point where you have thousands of others in your networks. So, every time you share, say, a blog post with them you will get some clicks. And they'll be good clicks from people in your target demographic.
SEO is more detached and calculating
With search engine optimization on the other hand you're somewhat removed from your audience. You have to be more calculating about it. If you really want that Google traffic then you do have to think long and hard about the keywords you're aiming to rank for. Will they supply enough traffic and can you get on page one for them? If so, what do you need to do in your article to achieve this? How often do you need to sprinkle them throughout the post?
Obviously you want to be writing primarily for humans, but you do have to consider the search engines. That makes it less spontaneous and satisfying in some ways.
Sure, that work may well pay off brilliantly, and for a very long time. But it may just come to nought, too! Worse still, you might be going gangbusters for a while and be over the moon, then all that traffic disappears overnight when Google updates its algorithms yet again. When that happens it's very dispiriting.
Then there's the fact that optimizing your site for search engines is inherently solitary work. And social media is by definition social. It involves human contact. Yes, it's not as satisfying as the real old fashioned kind. But its still better than nothing!
Being an SEO is kind of like being a composer as opposed to a musician. The former spends all that time crafting the melodies. But the latter has the fun of playing them to a live audience!
Both are needed, though
Of course you can do both, and you should. And I think you should spend more time and energy on the latter activity for the reasons cited above.
Then there's the fact that social media engagement complements your SEO anyway. By building those valuable relationships with other bloggers and webmasters in your niche you are sure to end up with more shares of your content on social networks as well as the odd one way voluntary backlink. All those things are factored into Google's estimation of your site and will surely help it crawl up the rankings over the long term.