The main difference between an IRA and a 403(b) is the type of account. A 403(b) is set up by the employer while the IRA can be set up by an individual.
Eligibility
Eligibility for a 403(b) depends on the employer. Except for a couple of small restrictions, almost anyone is eligible for an IRA.
Contribution Limits
A 403(b) has a much higher contribution limit than an IRA. In 2021, a 403(b) annual contribution limit is $19,500 while an IRA annual contribution limit is $6,000 (and a $1,000 catch-up limit if you are 50 or older).
Investment Selection
IRAs typically have a much broader selection of potential investments than 403(b)s, which may be limited by the plan.
Fees
Administration fees for 403(b)s are much higher than an IRA.
If you don’t have a 403(b) plan available, fund an IRA. Many small employers, ministries, or faith-based organizations don’t have the money or experience to offer a retirement plan at all, let alone one with either a basic or matching contribution. This means you have to start your own retirement plan.