Confronted with Chinese characters while learning Japanese

As I started learning Japanese from last year more seriously than before I faced a few times the situation that I saw Chinese characters and got extremely curious about their meanings.

Is it being at the airport, running through Chinatown or working in a factory, it's so easy to be confronted with Chinese characters. But when you are studying Japanese it can be confusing: You notice characters which look familiar and some you've definitely seen before. You even know their Japanese readings and also what it means... But you don't speak any Chinese language!

But as an learning addict your mind wants to figure out the meanings. Looking at food menus you often get an idea on what it means, but on the other hand I noticed some train stations in Singapore which I couldn't understand properly.

Then I was in a factory and I could read characters for example for milk. The characters don't feel like 'unreadable' anymore, it's amazing. 

You even start looking up characters via radical search with your Japanese dictionary app (e.g. Jsho) only to find out that the character is only not really used in Japanese. For example I found this on a package of a box:  姆

Looking at the radicals it means "female" and "mother", so it made me curious of course.

Also, I guy from Hong Kong I met in Australia told a good example of how meanings of a Kanji can differ by the example of 湯. In Japanese it's ゆ and a common term for hot water - especially at places like onsen. However, in Chinese the meaning would be "soup" (tang). I found that quite interesting. 

I'm aware that there are lots of examples, so if you know an interesting one, just let me know in the comments.

And how do you feel as Japanese learner being confronted with Chinese characters? Okay, of course it's clear to me, that Japanese Kanji are based on Chinese ones, so maybe I should rephrase: Are Chinese words confusing Japanese learners or make them rather curious?

Let me know^^