What is the difference between 0345 and 0845 numbers?

0345 numbers are the Mirror Numbers of 0845 numbers, and you can only obtain the 0345 equivalent if you already have the 0845 number. 

0345 numbers are UK wide numbers (like 01 and 02 prefixes), and are therefore cheap to call (they can often be free or included in call packages.) A set up fee will be charged and there will be a monthly fee charged depending on the amount of calls routing through the number to UK landlines. 

0845 numbers are local rate numbers which cost more to call. As it costs more to call these numbers, they can often be free to set up and point to a UK landline.