In this example, the speaker will first go to the gym. After that is finished, they will visit the post office. Here are more examples:
“Then” is frequently used as a casual way to say “therefore” or “in that case.”
It is also used in this way to show frustration or annoyance at someone else's action or decision.
The set phrase "Well then ~" is common as an informal way of making a suggestion.

”Than” is basically used when comparing things or situations.
In the last example, someone's arrival is compared to when the speaker thought they would arrive.
This usage is similar in meaning to “instead of.”
At the beginning of a sentence, it is used together with "rather."
Used with “other,” it means "except for" and expresses that something or someone is not included.
Here, the laptop is not included in "anything."

Finally, let's look at some expressions that use these two words.
Meaning: at that specific moment
Meaning: something that happens late is better than something that never happens
Meaning: preparation is important in order to avoid trouble or inconvenience in the future
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