what is the difference between 250,000/500,000 and 500,000/500,000 liability limits

In auto insurance, liability limits are offered as a single limit or, as in your case, “split limits”.  The $250,000/$500,000 allows a payment of up to $250,000 per person for bodily injury and a total of $500,000 per accident.  If there are multiple injured parties as in the above case, the insurance company can pay the per person limit of $250,000 for the one injured party.  They will then only pay $250,000 of the $350,000 in injuries.  That meets the per accident threshhold.

If you have $500,000 per person for injury, the one injured at $250,000 will get that amount.  But since the per accident limit remains at $500,000 the most the other party can receive is again $250,000.  The insurance company can choose to pay the $350,000 to the one injured party, but they would then only pay $150,000 to the other party, to meet the $500,000 threshhold.