▲你的两个句子中的分号，可以理解为转折关系（当然也可以理解为普通的并列关系）：

Everyone faces changes; different ones at different times.

Everyone faces changes but different ones at different times.

Everyone faces changes and different ones at different times.

每个人都会面临改变，只是不同的人会在不同的时间（面临改变）。

We all handle the same challenges differently; we all have different results.

We all handle the same challenges differently but we all have different results.

We all handle the same challenges differently and we all have different results.

我们都会用不同的方法处理同样的挑战，但我们得到的结果会不尽相同。

▲分号的用法

以下内容摘自《张道真英语语法大全》：

1793 分号有以下用法：

1. 把没有连词连接而意思上都有联系的句子连接起来 (可以用句号，但这时意思会被断开；也可用逗号，可能力量较弱不能把两句拉在一起；也可用冒号，但现在这样用时比过去少了)：

It won’t last long; it’s too weak.

He is a clever fellow; even his enemy admits it.

I love you; I worship you; I want you.

He is content; he lives happily.

2. 把内部包含有逗号的两个句子连在一起 (这时不宜用逗号)：

Dick is a generous, large-hearted person; but John, Mary and some of his friends are selfish people.

 (Cf. Dick is a generous man, but John is a selfish fellow.)

Alan ran his business carefully, methodically, and efficiently; and he was a great philanthropist, too.

He has three wives：one, who married him 20 years ago; a second, who was a rich widow; the third, who has already married five times.

3. 用在后面跟有逗号的连接副词之前：

He studies hard; moreover, he has to work for his living.

He has squandered all his wealth; therefore (或as a result), he has to beg his bread.

4. 用在两个并列从句或两个短语之间 (这时也可用逗号，但对比性较弱)：

We know that country life is more quiet than city life; that it is more healthful; that it is happier.

To work eight hours; to sleep eight hours; to do other things eight hours—that is the best way for man.

That depends upon who do it; how they do it; and when.

5. 用在such as, that is这类词前：

We learn several subjects; such as (or e. g.) chemistry, and physics. (These are some of the subjects we learn.)

We learn several subjects; that is (or i. e. viz, to wit, namely), chemistry, physics, maths and biology.

 (These are all the subjects we learn.)

—在这种句子中也可用逗号或冒号代替分号：

We learn several subjects, namely chemistry, physics, and mathematics.

We learn several subjects：namely, chemistry, physics, and mathematics.

We learn several subjects, namely, chemistry, physics, and mathematics.

—但在下面这种句子中逗号、冒号或分号都不需要：

We learn such subjects as chemistry and physics.