IRC Code Section 105 covers HRA, while Code Section 125 does not. The main difference is how the IRS can look at the plan and reimbursement features, as well as what can and cannot be excluded from taxable income. This is all connected to the taxability of benefits.
Alternatively, FSAs are covered under Code Section 125. Depending on the type of expense being reimbursed, an employer can use an FSA covered under Code Section 125, as well as Code Section 105, so long as it is treated as a medical plan. Coverage under the Code Section 125 allows for the reimbursements to be non-taxable. It is important to note that a medical plan under Code Section 105 is not always an FSA under Code Section 125. Code Section 125 implements the “use it or lose it” rule, which is more restrictive. Generally any Section 125 plan will also be covered under Section 105, but only flexible spending arrangements under Section 105 are covered plans under Section 125.