You don't say if you, yourself, are sitting down with her and reading with her and to her. It sounds from the post as if you're expecting her to pick up a book by herself and sit down with it on her own. Maybe not, since your son loved books -- I assume that means you read to and with him.
If she is very active, she needs to see you get a book, tell her with great excitement that "It's reading time!" and call her over to sit on your lap (or next to you, or on the floor, whatever) and read to her. Be warned: She may be wiggly; she may not want to sit at all. That sounds like it'll frustrate you but it is FINE. Let her wander around the room or play with toys while you read to her. Don't fuss at her for not sitting nicely; she's still listening in her own way. Sometimes call her attention and say "Look at this pretty picture!" Or "Here's a picture of the cat in the story!" and hold the book up for her to see, but if she is on the other side of the room that's fine. She is still hearing your voice, using words. Do this a lot. I mean, a huge amount. She will eventually wander over and want to sit. Use your finger to trace the line of the words and eventually she may do that too. Make books, read by you, part of your naptime routine, part of your bedtime routine, part of the routine in the morning (a book in bed before she gets up or a book right after breakfast).
It sounds as if your expectations are not quite right for her age and very active stage; don't expect her to sit down quietly on her own after picking out her own book or to sit quietly every time she sees you with one. If she sees you reading to her all the time, she will be interested in the stories. But don't force her onto your lap or tell her she must sit to have a book; she will start to associate books with being forced to be still and that will make books a negative thing for her. She can still listen while she moves around.
Please dump the TV. All of it. Please go to the web site of the American Academy of Pediatrics; they are against ANY screen stuff (TV, computers, hand-held devices like your iPhone) for kids under age two. And personally -- I think one reason my daughter was a huge fan of all books by the time she was about three is because we didn't have her watch any TV except maybe one video at the weekends. That's it. TV provides all the "imagination" for them; TV is passive. Books and CDs of books are active-- they must use their brains.
You say that "TV and books are the things I've been watching her with" but I'm not quite sure what that means. Do you mean that you either are putting books out for her or have the TV on? It sounds like she is already at the stage of ignoring the TV as mere "background noise" so ditch it. And you have to engage with her constantly by reading to her, talking to her and playing with toys with her. One trick, by the way, is to take some of her books, curl up with them, and "read" them to yourself but laugh a lot or say, "Oh that's so funny" and other things - she will get curious and come over to you to see what's so amusing.
Recite rhymes to her while she is in that constant motion you mention. Use nursery rhymes when you throw a ball with her; they have rhythm and so does tossing a ball. Sing and talk and recite rhymes to her as you push her on the swing. Kids need to hear language a lot and need the rhythm of rhymes as well as the longer sentences of stories.
Be sure too that the books you now have are appropriate for her. If they are too babyish (just pictures and no words or one per page) or too advanced they will bore her. Do you take her to the library? Make it at least a weekly trip if not more often! Hang out in the children's section for a long while-- dont' just get books and leave. Ask the children's librarian what books are engaging and fun and appealing to an active kid her age.
Please do not make the huge leap to "maybe she's ADD/ADHD." Parents now tend to jump to that if their child isn't doing certain things by certain times, but the parents' expectations often aren't totally realistic, or the child's personality is just not what the parents expected. You have a very physically active child and that is normal at this age. To keep her brain engaged you'll have to be extra active alongside her and talk and read to her much more than you might have done with your son, whose personality might be more inclined to sit down with a book on his own.
