word choice - Are "like" and "such as" completely synonymous?

"Like" and "such as" seem to fit the exact same sentences:

I want a cookie like that

I want a cookie such as that

There are plenty of variations where they differ:

I like cookies

I, like, eat cookies

I use cookies as such: Eat them; bake them; store them.

But the usage I am interested in is when they compare one thing to another. When is it best to use one or the other? Are there different connotations? Other examples:

A friend like you is a treasure / A friend such as you is a treasure

I hate tests like these / I hate tests such as these

No one cares like you / No one cares such as you

The last "such as" seems iffy to me.

Answer

Both like and such as can be used to introduce examples. This is what's going on in these two sentences that you gave:

A friend like you is a treasure / A friend such as you is a treasure

I hate tests like these / I hate tests such as these

However, such as cannot be used to join two things which are similar---only like can be used in this case:

No one cares like you / *No one cares such as you

In this sentence, the intended meaning is something like No one cares in the way that you do, and only like can be used for this purpose.

Note that I'd put for first example in this category:

I want a cookie like that

? I want a cookie such as that

It seems to me that this means I want a cookie similar to that one, and such as strikes me as ungrammatical to use here.