Clearly there has to be a difference between the two, or they wouldn’t have two different names. Right?
Leggings and tights are very similar in that they’re made of stretchy, soft materials that basically grip onto your legs because of how tight they are (which is sort of funny to think about, considering how comfortable they are). There are really only two big differences between leggings and tights, the first of which being that leggings are footless, tights are not.
In a way, tights are like half onesies, in that they cover your feet and go halfway up your body in order to cover your legs. A major benefit to this is that it basically eliminates the need for socks. They also create a seamless transition from where they would end if they were leggings and where socks would start. This allows for you to be able to wear whatever shoes you want to, basically, without worrying about whether or not its going to look awkward with the tights. Leggings, on the other hand, cut off usually at the ankle, so they aren’t nearly as seamless as far as transitioning into socks. This might look a little bit awkward if you decide to wear lower rising shoes.
The other major difference between the two is thickness. Tights tend to be a lot thinner than leggings, making leggings the better option for winter clothing and tights the better option for the summer. This doesn’t just effect when to wear each item seasonally, though, it also effects the look. Due to the thinness of tights, they’re usually a lot less opaque and almost always will show your legs at least somewhat through the fabric. This isn’t really an issue unless you’re looking for something to wear that is going to be practically 100% opaque. What is an issue, on the other hand, is how easily tights can rip with how thin they are. You always have to be extraordinarily careful or you risk having a run in your tights (and no one wants that). The good news is that tights are fairly cheap (usually a lot cheaper than leggings, but it depends on where you shop, the color, the size, and a bunch of other factors that effect the price), so they’re a lot easier to replace than leggings. You have to option, also, to buy them in packs, which basically just lengthens the amount of time your tights will last (which is a huge plus).
In summary, the two things are very similar, but are set apart by the fact that one has feet while the other does not, and one is much, much thinner and less durable and opaque than the other one. Either one can add on to an outfit in a way that could not be achieved otherwise, and the one that you wear is entirely up to you.