Usually, under the Variable Set related list on any catalog item form, the names of catalog items are shown as a hyperlink. Clicking on the name of the variable set will open the respective record. However, sometimes these names are not shown as a hyperlink when the language of the instance is changed.
The hyperlinks are visible based on the translation present for the names or not. If there are no translations present for any of the variable set names, then even in a language other than English also will also be shown a hyperlink. When it is a multi-lingual instance, the name of the field will first be searched on the translation tables to fetch the relevant translation. In this case, it will search from sys_translated table.
However, if there are multiple variable sets on the catalog items (say 3), and only 1 of those have the relevant translation present on the sys_translated table, only that variable set name will have hyperlink shown under its name. For other 2, no hyperlink will be shown for those.
For multi-lingual instances, separate translation records need to be created on sys_translated table, for each of the variable sets, for each language other than English.