到(dào)期(qī) means ‘due’ and 过(guò)期(qī) means ‘expire/to exceed the time limit’.
到(dào)期(qī) is prone to be used in the field of loan, contract etc, while 过(guò)期(qī) is more likely to be used in the field of food and product. For example,
合同即将到期
Hétong jíjiāng dàoqī
Contract be about to expire
‘The contract is about to expire.’
食品即将过期
Shípǐn jíjiāng guòqī
Food is about to expire
‘The food is about to expire’
