There are two basic types of savings; tax deferred savings like an IRA, or a 401K, and post tax savings like a savings account, or an investment account. Both have their place. Tax deferred savings have the obvious advantage of reducing taxable income and saving for retirement while you are working. They have the potential disadvantage of triggering recognition of significant income if not treated properly after you pass on. Avoiding recognition of income (where the IRS counts the value of the entire IRA for income tax purposes) may limit how the IRA can be distributed after you die.
Regular savings can be passed on by naming a death, payee or through a will or trust. Income will probably not be recognized unless some annuities are part of your savings plan.
Placing savings into an irrevocable trust can help qualify you for needs based benefits like TennCare long term (nursing home) care without spending all your money first.