碰巧 = coincidence ; things just get right by chance 我在書店碰巧找到這本絕版書 剛好 has the meaning of "just right, just fits perfectly". Example: 這雙鞋的尺寸剛好。You won't use 碰巧 in this case. In some cases, both apply : 你手機壞了，我碰巧/剛好有隻備用的借你。 碰巧 here means "the spare phone is not particularly prepared for you, it just happen that you are in need of one" 剛好 here means "yours is broken and I have a spare. Everything just fits perfectly!"

在教室 我剛好/碰巧遇到老師 在電梯裡 我剛好/碰巧遇到我爸 剛好 -we use it more commonly 他們在打籃球 但籃球剛好打到我 <--It might sound a little strange if you use 碰巧 in this sentence.

两个词意思相同。 如：你看见Jay了吗？看见了，二十分钟前我刚好/碰巧在校门口遇见他。但是有时不能互换，因为搭配不合理。如：我刚好有二十元钱。不能换用碰巧。

碰巧、刚好=恰恰

Almost the same