Do generic shampoos and detergents differ much from name brands?

I’m on a tight budget, and shop a lot at the Dollar Tree. I buy almost anything there, including shampoo and conditioner and laundry detergent. So far, it has been quite economical. But it has me wondering if the generics, specifically shampoo and laundry detergent, are of a lesser quality than the name brands. Will the shampoo damage my hair? Or will the laundry detergent not really clean my clothes as well as, say, Tide?