I am using tags field:
When I switch language to translate, from what I see, the only option is to erase other language’s tag and create new, but this way it’s like new tag, and also filtering by tags in page template shows all tags in all languages.
Is it possible to translate exact tags?
It all depends on your use case, for example, you can set fixed options for the tags field: https://getkirby.com/docs/reference/panel/fields/tags#limit-input-to-options
Then you could show different display values, while the same value gets stored. And then from that, you could again display the language specific translations in the frontend.
Thank you, that would help a lot, only still need ability for client to change tags (categories) in panel, how is it possible to achieve?
Could you please be more precise regarding the exact requirements?
You could let the client define the options somewhere and then query the options from that fields, but without really knowing what you want to achieve, its hard to come up with the best solution for the use case.
I would be hard to translate things where you don’t know what the options are in advance.
Ok, will describe use case. Client needs to show projects, we will have page with all projects, and also we need to filter them by categories. And there can be new categories later, or some changes in existing, so would prefer to be able to edit and translate categories in panel, not in code, as then client can do it in one minute, instead of having to explain to me, wait, then check.
From what I understand about Kirby, probably solution might be to create parent page “Categories”, and then create children as categories, that could be added as “related” in fields of projects. But then another question is how to have nested categories? 
From what I understand, it would make sense if you define your categories somewhere, for example, using a field in site.txt. That could for example be a structure field with values and translations.
In your project page, you could then query the options defined in that field in a tags or multiselect field.
In the template, you could then query the translations based on the values stored in the project.
Tbh I miss this functionality too. In other CMS’es this functionality is often called “taxonomy”.
In Kirby we have tags, but then we somehow lack a central “management” screen to manage (CRUD) those tags. And they are hard to do right in a multilingual context for an editor’s point-of-view.
As I see it, the hardest part is that you can “create” a tag/taxonomy term (from a field) whilst creating new content. If that isn’t necessary, you can go a long way with selects.
Another hard thing is taxonomies with hierarchies.
Edit: I exchanged ideas with @bastianallgeier about this during the next-fase. Some of it was written in notion (dd 8/8/2017 
): https://www.notion.so/Kirby-taxonomy-c3565ecb974f438e8a39096652582841