
I knew about the difference between coffee and yes cups but got curious when she started chattering about different types of tea using different styles of cups. So I found this.
https://blog.teabox.com/good-tea-needs-good-teacup
Then I decided that it didn't matter that much since I drink ice tea by the liter to stay hydrated and nobody's going to be building me a temperature and humidity controlled tea warehouse.

Keep in mind that as this webtoon shows there are many kinds of tea and tea bags aren't presweetened like those instant tea packages. Black tea should be steeped in boiling water which is 212* F but not for longer than 5 minutes or it will become very bitter. Green teas need to be steeped in a lower temperature hot water, about 170* F. If you don't have a candy or meat thermometer to test the temp just let it sit for a few minutes to cool a bit. And I think I will stop there as this is your first foray into actual tea and you probably don't need or want the many, many details of the wondrous world of tea right now.
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http://www.mangago.zone/read-manga/the_duchess_50_tea_recipes/hs/mpn_chapter-2132863/pg-2/
Which one is the tea cup? I'm guessing the wider one. but...
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They both just look like cups to me. Personally as long as the tea and/ or coffee is good, I don't care what cup I drink it from.