I notice that some receipts have the words "Cash Paid" while others have "Cash Tendered". Are there differences between them? Can they be used interchangeably? Are there situation(s) where one of them will be more suitable than the other?
The two phrases are often used interchangeably, in a conversational context. For casual usage, cash paid is more informal and more common than cash tendered. But there is a difference in meaning between the two phrases, in accounting, specifically for cashiering and bookkeeping.
A few background details
In bookkeeping there are Accounts Receivable (A/R) and Accounts Payable (A/P). Money owed to you accumulates in A/R. Bills and debt obligations owed to others is tallied under A/P.
Cash tendered is a sum of money given in payment. It may not be equal to the exact amount owed. Using cashiering as an example (which is part of a business's A/R), cash is presented as payment for a service or to settle an outstanding bill. That cash is tendered. If it is exactly equivalent to the amount of money owed, then cash tendered is equal to (the amount of) cash paid.
If the amount of cash tendered is greater than the amount owed, a credit balance is owed to the customer. The credit might be change, or it might be entered onto the books of the business as an A/P item due to that customer in the future. This is a case when cash tendered is greater than cash paid. Note that cash tendered minus cash paid equals change returned to the customer or the sum entered into the books as A/P.
If the amount of cash tendered is less than amount owed, the business might accept this money. If so, A/R would be reduced by the amount of cash tendered. Often the terms of the transaction will not allow cash tendered to be less than the amount due though! Examples are restaurant bills and installment payments e.g. credit card monthly charges or a mortgage payment. If so, none of the cash tendered by the customer will be accepted by the business. This is a scenario where cash tendered is greater than zero while cash paid is equal to zero.