The Special:Log shows the block expiry depending on the user input. For example @jayvdb did some tests with different block times and got the following entries and the values he used are visible in the blocks/duration section of the API request.

The UI should always use the expiry given and depending on it's value always show 'infinite' (if there is no expiry), the date in whatever format the wiki uses (if expired) or a human readable delta. This way it's irrelevant if the user said “in 10 days” or “on 14th of January”. And there seems to be already some time of conversion as the 500 hours were originally converted to 20 days and 20 hours (obviously less over time). But that conversion was unable to detect “tomorrow” and just displayed the date directly (but the API understood what it meant).