What is the difference between 欢喜 and 快乐
喜 delight; pleasure
樂 happiness; joy

If you do not know the difference between 喜 and 樂, you can realize it from their antonyms.

It is pretty often to use two opposite words together in a Chinese phrase.
For example, (天地)玄黃, (天地)良心, (陰陽)怪氣, (陰陽)交錯, (緩急)(輕重), (緩急)相濟.

It is the same case in 喜怒哀樂.
There are two pairs of words here, which are 喜怒 and 哀樂.
Since the question mentioned 喜 and 樂 of 喜怒哀樂, let's just focus on this phrase. The antonym of 喜 is 怒 (anger), and 哀 (sorrow) is the opposite of 樂.

I think you certainly know the difference between anger and sorrow, then you should know the difference between 喜 and 樂.



「喜怒哀樂」的出處：《禮記·中庸》


  天命之謂性，率性之謂道，修道之謂教。道者也，不可須臾離也；可離，非道也。是故，君子戒慎乎其所不睹，恐懼乎其所不聞。莫見乎隱，莫顯乎微，故君子慎其獨也。 喜怒哀樂 之未發，謂之中；發而皆中節，謂之和。中也者，天下之大本也；和也者，天下之達道也。致中和，天地位焉，萬物育焉。


《中庸》第一章

上天賦於人的氣稟叫做性，順著本性去做叫做道，修明道的本末無偏私，就是教化。這個道是片刻不可離開的啊！如果可以離開，那就不是正道了。所以，君子在人看不到的地方也要警戒謹慎，在人聽不到的地方也常惶恐畏懼。沒有比隱暗處更顯現的，也沒有比細微處更顯著的，所以君子在獨處時特別謹慎。喜怒哀樂的感情在沒有發動前，叫做中；如果情感發出後都合乎節度，叫做和。中，是天下事物自然的本體；和，是天下人人共行的道路。能夠完全達到中和的地步，天地便可安居正位，萬物便可順遂生長了。