If you claim that something is true, you say that it is true, although you may not be able to prove it or to make people believe you.
1. ‘Did he really kill six men?’ Kay asked. “That’s what the newspapers claimed, ’ Mike said.
2. He claimed that he found the money in a forest.
3. He claimed to be a Scot but had a powerful Liverpool accent.
If you pretend that something is true, you try to make people believe that it is true, although you know that it is not.
4. The rest of us stood around for a while trying to pretend nothing had happened.
5. He could pretend, perhaps, not to recognise them.
6. ‘You don’t want to spend your life with me,’ Joyce said, ‘so why pretend?’