Kids do like to pick up things when they are in a shopping place but you should not just restrict them. What I do with my daughter is I give her a small basket and I ask her to pick up whatever she wants. If she picks up something she does not need then I explain to her that we are at that place to buy things we really need for us. I let her pick chocolates. Maggi, chips etc. which is for her use. May be sometimes she picks up her soap and shampoo also. This way she takes it as a responsibility and shopping becomes interesting for both.

Though still sometimes she does bug me but ultimately she is a kid and she will do that.

My daughter had been like this. Once I had almost lost her in a mall. Within 2 minutes time she was at the other end of the mall. And she would never walk along with me. If I tried ti put in the trolley so that she could not go around she would start screaming at the top of her voice.

Only of thing is that though she kept picking up things and putting it here and there she never ended up damaging anything. Thank God. I had been doing a lot of research on how to improve her behavior but nothing seemed to work. With time she herself started behaving. Now also she picks up things in shops but when I remind her she puts it back. And when we go grocery/clothes shopping she picks up things for herself.

She also helps me in choosing stuff for me.

My son is opposite. He will just sit at a place. I want him to be active. Even when we take him for shopping he will either walk by my side for stand at one place gazing people. I would love my kid to be a bit active

My son also is a big trouble while shopping. Thank god he has not broken anything till now but I have to be alert every sec. One of the tricks that works for me is that I buy him chocolates and chips for him and I do my shopping while he is busy eating his favorites.
I hope this behavior of his goes as he grows up.