I guess they have same meaning with the way to convey.

I would like you to suggest some example sentences for it.

ために and ように　actually these are kinda polite expression to express the way for you to come true something . 

お金を稼ぐために、働く。 "you work to earn money"

お金を稼ぐ（ように）働く。←This is not correct for usual conversation.

actually before the word ために, the verb"concrete action" should be put usually.

Then "ように"..., mostly "the status" which 主格 is longing for should be put before ように.

金持ちになるように働く。　"work to be a rich man."

it can express the "stustus" which you want to be.

Then "ように" should be used for negative stustus which you don't want being.

”貧乏にならないように” before ように, negative word could tend to be put often.

Of course "貧乏にならないために" this could be right,however japanese people seldom use such way to tell.

~しないように←this is natural and correct expression.

anyway, 金持ちになるために働く。　This could be also OK. it can express the concrete action for you to come true.