The words 终于(zhōngyú) and 最后(zuìhòu) in Chinese can be difficult for beginners to distinguish, because both of them can mean "finally" or "in the end". Remember that there is a lot of overlap between these words: they are not totally separate in meaning.
对于初学者而言，“终于”和“最后”这两个词很难区分，因为两者都是“finally”或“in the end”的意思。注意这两个词之间有很多重叠部分，它们在意义上几乎无法区分。
However, there is some difference between the two. The key difference is that 终于 puts more emphasis on "finally" as in "something is finally done", whilst 最后 is simply "the last" or "in the end". Let's have a look at each word in turn.
不过，它们之间还是有些不同的。主要的不同之处是“终于”更加强调“something is finally done”里的“finally”，而“最后”仅仅是“the last”或者“in the end”的意思。我们分别看下这两个词。
终于(zhōngyú): finally, at last
The word 终于 has a close range of meanings: "at last, in the end, finally, eventually". 终于 can be used to emphasize that a lot of time has passed or a lot of effort has been expended, and something is finally done.
“终于”这个词有着广泛的相似意义：“at last, in the end, finally, eventually”。“终于”可以用于强调“时间已经过去很久”或“付出诸多努力后事情终于完成”。
Because of these, 终于 sometimes implies that what happened was desirable or wanted.
Let's have a look at some example sentences for 终于:
tā zhōngyú láile.
He's finally here!
tā dāng lǎoshī de mèngxiǎng zhōngyú shíxiànle.
He finally realised his dream of becoming a teacher.
tā yào fǎnghuá de yuànwàng zhōngyú shíxiànle.
His wish to visit China has at last come true.
wǒ zhōngyú shíláiyùnzhuǎn le.
Finally things are looking up for me.
In each of these situations, something has finally happened that seemed to take a lot of effort or time.
Remember, though, that 终于 isn't totally distinct from 最后, as it can also mean "at last" or "in the end", and be used to talk about neutral or bad things happening:
记住，尽管“终于”和“最后”没有多大不同，它也可以表示“at last”或“in the end”的意思，还可以用于谈论发生的中立或不好的事情。
nà wèi yùndòngyuán zhōngyú jī jìnle yī qiú.
At the last moment the player was able to hit the ball in.
tā zhōngyú yóu jù fù lún wèi chìpín.
In the end, she fell from great wealth to abject poverty.
最后 (zuìhòu): the last, in the end
The word 最后 has meanings like "final, last, finally, ultimate". As mentioned above, there's clearly a lot of overlap with 终于.
“最后”这个词有着“final, last, finally, ultimate”的意思。如之前所说，它和“终于”有很大部分的重叠。
The difference is that 最后 is usually neutral compared to 终于. It simply states that something happened last or in the end, but doesn't necessarily imply that it took a long time or a lot of effort. It was just the final thing that happened.
zuìhòu, wǒmen de xiàngmù chéngle pāimàihuìshàng zuì tèbié de yīxiàng.
Finally, we come to the most special item in this auction.
zhè shì zuìhòu yī zhāo.
This is a last resort.
zuìhòu, tāmen zhǐdé fàngqìle.
In the end, they had to give up.
zuì hòu tā xiǎng qǐ le tā de míng zì.
His name finally came to her.
Hopefully you now know that whilst 最后 also means "finally" or "in the end", it doesn't have the implication that this was the result of a long wait or a lot of effort like 终于 does.
但愿你明白，虽然“最后”也有“finally”和“in the end”的意思，但它没有像“终于”那样有“经过长时间等待或许多努力后才有结果”的隐含意义。