Разница между двумя англ словами.

Почему вы переводите прилагательные наречиями?
Carefully не только "осторожно", но и "тщательно". Т. е. не жалея усилий.
Neatly - аккуратно, т. е. опрятно.
Вот вам примеры:
https://context.reverso.net/перевод/английский-русский/neatly
https://context.reverso.net/перевод/английский-русский/carefully

neat
tidy, with everything in its place:
Your house is always so neat - how do you manage it?
She likes everything neat and tidy.
You have such neat handwriting.
They did a very neat job stitching up your knee - there's hardly a scar there.

Neat people like to keep themselves, their house, and their possessions tidy and in good order:
Hassan is the neatest child I've ever met - even his shoes are clean!
I try to be neat, but my husband is a slob.

careful -
giving a lot of attention to what you are doing so that you do not have an accident, make a mistake, or damage something:
Be careful with the glasses.
Be careful where you put that hot pan.
Be careful to look both ways when you cross the road.
Michael is a very careful worker.
After careful consideration of your proposal, I regret to say that we are unable to accept it.
He's in a really foul temper so be careful (about/of) what you say to him

dictionary.cambridge.org

neat - ото больше отношение к внешнему виду - аккуратный, чистый.
careful - это ко всему бережный, аккуратный, осторожный.