Both breach and default refers to situations when the parties do not comply with a condition of a contract. Though, there are differences between them.
Default is the non-compliance with any provision of the contract. It includes several actions and omissions by the borrower. The occurrence of a default entitles the creditor to take certain steps otherwise not permitted, including the termination of the contract.
Breach refers to the non-compliance with a material condition of a contract. It usually results in the termination of the contract. Also referred to as material breach.
In practice, the difference is that the default can be cured. If it is cured, then you do not have a breach. Cure is a way to circumvent remedies.
If the contract goes into non-curable default, there is a breach. Then comes remedy. Remedy is a form of relief obtained from the court as a rectification of the breach.