Both of these structures are used to express doing something in order to achieve some result or state.
٩(◕‿◕｡)۶
～ように．．．
This is used to express that you’ll be doing something (…) in order to achieve a good, non-problematic situation (~).
Ｖる・Ｖない・Ｖできる ＋ ように
歌が上手になるように、毎週末カラオケに行きます。
In order to improve my singing/get better at singing, I go to karaoke every weekend.
友達をがっかりさせないように、お土産を持っています。
In order to NOT disappoint my friend, I brought a gift.
早く起きられるように、アラームを設定します。
In order to wake up early, I set an alarm.
雨が降らないように、てるてる坊主をつるしました。
So that it won’t rain, I hung a teru-teru bouzu.
In the above examples, by using ように you are implying that there’s some lack of control over the actual outcome. If you feel that the result is more guaranteed, however, you should use ために – it’s more for “in light of A, B” where A results in B.
Unlike ために, ように is used when you cannot directly control the outcome. It’s better to use the potential form of the verb, or a verb like なる. You can also use ように to talk about something that’s definitely out of your control, like the weather （雨が降れないように…）, as seen in example 4.
If the resulting situation is a state, ability, or not fully under your control, use ように (with potential or non-volitional verbs).
ため(に)
This is more commonly used to express intentionally aiming for a purpose (that you expect to achieve/happen). You’re not just hoping that something will happen, you are expecting it.
Can be translated as “For the sake of (A)” or “in order to (A)”.
Vるため (plain or dictionary form)・Nのため
日本語が上手になるために、毎日勉強しています。
In order to get better at Japanese, I study every day.
試験に合格するために、毎日2時間ぐらい練習しています。
In order to pas the test, I reviewed for about 2 hours every day.
遅れないために、早く家を出ました。
In order to not be late, I leave the house early.
忘れないために、メモを取りました。
In order to not forget, I wrote a memo/note.
ために can also be used with nouns!
家族のために、毎日晩御飯を作ります。
For the sake of my family, I make dinner every day.
It can also be used as a “modifier” when used with の instead of に, as in ための.
野菜を切るための包丁です。
A kitchen knife for cutting vegetables.
漢字を勉強するためのノートです。
A notebook for studying Kanji.
旅行のためのお金をためています。
In order to travel, I am saving up money.
Bonus: ため with past tense!
When used with past tense, it generally means “in light of (A)”, highlighting that (A) is the major event/thing (already happened) that resulted in – or will result in – (B). Can also be translated as “due to” or “because of”.
二年前、車を買うために、親からお金を借りました。
Two years ago I borrowed money from my parents in order to buy a car.
骨折したため、明日からしばらく仕事を休みます。
Since I broke a bone, starting tomorrow I’m going to take a little time off work.