"Useful" is more functional, necessary, practical and without emotion.
You often describe THINGS are useful, even if they are non-physical. Useful advice = to get something done, achieve something.
- useful travel tips e.g. make sure you get to the Eiffel Tower early, before the crowds arrive.
- useful recommendation e.g. that Joe is a good plumber in your area
- useful instructions e.g. those that come with IKEA furniture (well, maybe...)
- useful advice e.g. shortcut to avoid the traffic jam on the motorway
- useful tip for learning English e.g. try listening to podcasts
- useful idea e.g. ingenious way to use old plastic bottles to power a car!
- useful knowledge e.g. about first aid or how to fix a car
Plus some idiomatic uses, examples:
- "why don't you make yourself useful, and lay the table?"
(but I would still never say that a person is useful)
"Helpful" is more emotional, nice and kind. It is often used for PEOPLE and the THINGS PEOPLE DO. Helpful advice = makes something easier or lighter; it is supportive and nice (not such a yes/no achievement). Maybe I feel grateful and glad.
- helpful memory e.g. it was helpful that I remembered the way, otherwise I would have been lost
- helpful support e.g. Sarah did my shopping while I had a broken leg, it was so helpful!
- The exam was very difficult, so it was helpful that I had did so many practice exams in advance
- If your child has trouble sleeping, it is helpful to keep a bedtime routine
- My doctor gave me some helpful advice to lose weight
- It was so helpful that I could speak English during my holiday in Australia
- There's a helpful mnemonic to spell "rhythm": Rhythm Has Your Two Hips Moving
In practice, the definitions are not sooooo different, much advice can be useful and helpful. I am just trying to give you examples to get a feel.