Child Care / Dependent Care Benefits
"What is the difference between claiming a child care tax credit and utilitizing dependent care benefits where I work?"
The two are not mutually exclusive so you might be able to do one and still some of the other. A child care tax credit is where a married filing joint (or qualifying head of household taxpayer) takes a credit on their income taxes for a percentage of what they spend (up to certain limits) for child care. The intention is to offer a tax break for the expenses associated with child care required so the second taxpayer in the household can work.
Dependent care benefits are similar except it is a reduction of taxable wages for similar child care expenditures. As an employee (if your employer offers this) you have to make a "use it or lose it" election to have money set aside and you seek reimbursement of your expenses.