Native speakers don’t necessarily see the ように in ようになる or ようにする as the same thing as the ように in, say, ように見える, which describes what your perception or impression is like.

However, they are certainly related. If you choose to, you could analyze the ように in ようになる and ようにする as describing what the result of a change would be **like**.

Consider the following sentence as an example.

> 新聞が読めるようになる。<br>
You will be able to read newspapers.

新聞が読める describes the target state you think the person will be in when the change in question has happened. The connection with the other usage may be clearer when ように is used with a noun.

> 学者のようになる。<br>
You will be like a scholar.

This practically means the same as the following with みたい.

> 学者みたいになる。

In this usage, ように is not usually used with an adjective. There is a better way to say the same thing.

> 賢くなる。<br>
You will be smart.

> 綺麗になる。<br>
You will be beautiful.

When ように is used with a verb, that verb must refer to a state, not a one-time action or change. In the first example, a potential form is used to describe a state where you have the ability to do something. When a dictionary form is used, it is still understood as referring to a state, a habitual state to be more precise.

> 新聞を読むようになる。<br>
You will get into the habit of reading newspapers.

Note that ように cannot be replaced with みたいに in these examples with a verb.

ようにする works in the same way except you are the one who actively causes the change.

> 新聞を読むようにする。<br>
I will make it a habit to read newspapers.

The verbal phrase before ように still describes what the intended target state is like.

You can also use a more concrete verb instead of する.

> 新聞が読めるように毎日勉強する。<br>
I will study everyday so that I will be able to read newspapers.

This may make it easer to understand that ように describes what the intended target state is like because of the way it is translated into English. It now neatly corresponds to “so that.”

On the other hand, it becomes syntactically similar to a sentence like this.

> 貪るように毎日勉強する。<br>
He studies everyday as if to “devour” (books).

In this sentence, ように is used to describe how something is done as you perceive it, just like the ように in ように見える. We know that because it is hard to interpret 貪る as describing a habitual state, and it is much more normal to understand it as referring to an action to which the way he studies is likened. In short, you need context to determine in which meaning ように is used.