hurt vs. ache
I think in spoken English, "sth hurts." is more commom.

But I once found this expression below in a novel

The dogs followed at her heels, sniffing at the heavy grain bag she had fasten on her back. ......she tied the bag with a piece of rope she had carried in her dress pocket for just that purpose. That was an easier way to carry it. Her arms ached.

What's the difference between ache and hurt?

Question

hurt vs. ache
I think in spoken English, "sth hurts." is more commom.

But I once found this expression below in a novel

The dogs followed at her heels, sniffing at the heavy grain bag she had fasten on her back. ......she tied the bag with a piece of rope she had carried in her dress pocket for just that purpose. That was an easier way to carry it. Her arms ached.

What's the difference between ache and hurt?

Answer

'Hurt' would generally be used to describe a pain from an injury. For example if you were kicked in a game of football you would say your leg hurt. 
If you were tired, for example if you had carried bags of shopping for a long distance, you would say your arms 'ached'. 
Hurt is generally relating to more pain than something which aches, which is usually a lesser type of pain.