'Whether' and 'that' are conjunctions. They are used to connect clauses together.

We can 'whether' and 'that' to express alternatives and conditions. Have a look:

As you can see in the examples above, 'whether' and 'that' can be used as conjunctions. However, 'that' is used when there is a certainty. In other words, when we are sure about a condition or alternative, we use 'that.' Conversely, 'whether' is used when there is doubt about the condition or alternative.