Differences occur depending upon who is claiming the child for tax purposes. If the child is claimed by someone else (someone other than the person who purchased the bonds for the child), the dependent’s standard deduction applies. It is similar to the standard deduction that everyone else gets, but subtly different. The child can receive up to $1,000 of interest (in 2013) without having to pay tax.
Above $1,000, the child enters the single bracket with one more wrinkle. If the interest exceeds $2,000, the interest will be taxed at the parent’s marginal rate via the so called "Kiddie Tax," which is the name given to taxation of the investment income of children under age 19 (age 24 if the child is a full-time student).