Like v. such (and such as)

I am a teacher.

Therefore, I work as a teacher.

I work really hard on your behalf, and do not receive due recognition for my sterling effort.

Therefore, I work like a slave.

Am I a teacher? - Yes, I actually am -- As

Am I a slave? No, not really: I was exaggerating to win your sympathy  -- Like

So like means "similar to" or "resembling".

Such as

Look at the following sentence, which I would suggest is wrong: Countries like Germany are more popular with immigrants than countries like Britain.

What is a country that is "like" Germany? Austria perhaps (same language); or Sweden (wealthy, northern, full of blond people); the Netherlands (same miserable weather, similarly dodgy food, a language that is close to German). They are similar to Germany in some respects, I guess. But what countries are "like" Britain (the USA, Ireland, Australia, Canada...)?

Is like what the writer really meant, or did he mean countries such as Germany?  I suspect the latter.

If you use such as, you are giving an example,  not making a comparison or pointing to a similarity.

We should therefore write, Countries such as Germany, Italy, Greece and Hungary have a large number of Syrian refugees. Why such as? Because you are not saying these countries are alike, you are simply listing them as a set of examples. After all, these countries are not particularly similar to one another.

Rule: Use such as when listing examples; use like only if drawing attention to a similarity.

We are looser about this when speaking. Fine. But here we're talking about how to write.