Tae Kwon Do and Hapkido? Someone told me that there are both very similar but I've love to hear the right answer from someone who actually studies the art vs. someone who's just watched a few videos.
about as similar as basketball and football. Both played with a round shaped object, but totally different rules and principles.
"Pure" Tae Kwon Do and "Pure" Hapkido are going to be very different. While TKD and HKD schools vary greatly, keep in mind that TKD is, at heart, an art of punches and kicks. HKD, on the other hand, coming from Daito-Ryu Aiki-jujitsu, is a grappling art (throws and locks) at it's core. There are TKD schools that teach some HKD as part of the SD curriculum, and plenty of HKD schools that teach punches and kicks, but the two are distinct arts.
Putting the arts in perspective, it is the same as comparing Karate and Aikido, both are japanese but Karate focuses on punching and kicking with minimal hands-on self defence, where as Aikido's focus points are on locks and throws with strikes taking a back seat. Think Jean Claude Van Damme versus Steven Seagal. TKD and HKD are the Korean equivalent of these, although it has to be said these days TKD adopts some HKD self defence and vice versa if the instructor has cross trained. I myself teach mainly HKD but with backgrounds in varying styles I try to implement other training drills and techniques that I've found useful which in turn gives my students a wider exposure. I guess the point I'm trying to put across is that you should find out more about the background of the instructor as that would dictate the way that the particular style is taught. Just because the style says TKD doesn't mean necessarily there won't be any HKD in there somewhere. Hope this helps.
They are both Korean and they share some kicks in common, though the HKD way of performing the kicks can differ slightly. Aside from that, they are very different arts.
It's hard to find a pure Hapkido place, to be honest, but if there is a Kuk Sool place around you you may have some luck there. Hapkido and Kuk Sool are very very closely related, for a variety of reasons.