One thing you'll learn as a parent, is that children are different. Comparing one to another is like comparing a car to a strawberry: you can make lots of comparisons, but they don't tend to have much meaning. One child being social and liking other adults and one child being quiet and preferring to hang out with parents is entirely normal: you've just described my two children at an equivalent stage in their development, largely.
Many children will be clingy, and will be so for years. That's not at all a concern, absent other issues. My oldest, a four year old, is one of the most independent, smart, emotionally complex children you'd ever meet. He also refuses to go anywhere without us - no soccer practice, no martial arts, nothing, unless he can do it with a parent (not just a parent nearby). Who knows why - it's just how his personality is. If you are concerned about developmental issues, absolutely talk to your pediatrician about this - you should anyway just to get a good understanding of what she's going through and how to help her out.
At 18 months your child is still very early to really socialize - but that's not to say you can't help her out. Repeatedly taking her to situations where she can see other children playing, even if she doesn't play herself, will help her see the upside to playing with others: the laughing, the fun. It might take a long time, but in the long run she'll learn for herself how to have fun with others - particularly if you don't push too much. Let her observe, let her take her time to take it all in. Some children are more considerate, more thoughtful, than others, both in terms of feelings and in terms of wanting to take their time working things out.
And of course, at the end of the day your child might be more of an introvert. That's okay, too - many people are, myself to some extent included. If that turns out to be the case, then you can read up on how to help an introvert deal with social situations - both on this site, and in extensive literature. But I wouldn't jump to conclusions at 18 months - 18 months is simply so early for social development. Talk to your pediatrician, be aware of the social development stages she's going to go through, and keep an eye out for opportunities to let her learn about socializing through observation and opportunity.