Could these two words be replaced in any context or the meaning is not exactly the same? In particular if I'm listening a podcast or a radio show do hosts of this show discuss one theme after another or one topic after another? Or both words could be used in this context?
Learn English – the difference between “theme” and “topic”
synonyms
Related Solutions
There's some nuanced differences between the two. I came to know implies a more lengthy, substantial or involved process of acquiring knowledge than I learned. Synonyms of come to know include come to understand and become acquainted with, which are a little more distant from learn. For example, I came to know calculus suggests a drawn out process or a deeper, more personal relationship with the subject than I learned.
I don't know of any instances where I learned cannot be validly replaced by I came to know, but I do know that the exchange doesn't always work in the other direction. I came to know my neighbor is fine, but I learned my neighbor is unsemantic (people are not facts or ideas; you cannot learn them). I discount learned a lesson here because it carries a very specific meaning and uses learn in a different sense than usual. Cambridge even lists it as a phrasal verb (or at least thinks it merits a separate entry).
However, your question includes that after both phrases. Having that makes it about some particular pieces of information. In this case, came to know is a superset of learned, because both are completed processes of acquiring knowledge, and learning is about retaining specific facts. Because of this, I can't think of any cases where one works and the other doesn't if you include that.
Regarding your example, what's the context? Was the discovery of this information expedient and easy? Is the sentence intended to be merely informational? If so, use learned. Was it very difficult or time consuming to find out the woman's status? Is it the knowledge extremely important and worth emphasizing? Are you trying to avoid being prosaic? If so, use came to know. Compare:
I flew to Bangladesh to see my cousin. After landing, I went to a restaurant to meet her and her husband. Upon arrival, I learned that she was not in town. She had to make a business trip and would return the following week.
Tracking the billionaire's wife across Europe was no easy task, but I finally found out she was in Madrid, so I double timed it over there. Upon arrival, I came to know that she was not in town. I asked around at the likely clubs and bribed clerks at the upscale hotels, but if anyone had seen her they weren't talking.
If it comes to the sense of obtaining something by paying money, both "purchase" and "buy" are usually used interchangeably as a verb. Nevertheless, the use of "buy" is more common in daily conversational English than that of purchase. The use of purchase is a bit formal.
In some contexts, however, it sounds more natural to use buy instead of purchase such as I will buy him the book/let me buy you a drink.
Similarly, when you use these words as a plural noun, it's more natural to use purchase in some contexts such as she opened the bag of her purchases/her purchases were so heavy that she had to take a taxi. Besides, you often say in informal English when you buy something at a low/high price "it's a good/bad buy". "It's a good/bad purchase" sounds a bit weird.
Best Answer
When referring to something like a podcast or a regular column, theme refers to the overall subject of the work. "It's a weekly podcast about economics" is the same as "The theme of the podcast is economics". Topic, on the other hand, refers to the subject of an individual episode. "Today we have three topics: long-term interest rates, the Tokyo stock market, and last week's unemployment report".
In other kinds of short works, for example a stand-alone essay for school, "theme" and "topic" are generally interchangeable.
EDIT: as prompted by @Andrew below: For larger works, especially fiction or persuasive writing, the "topic" is the actual, literal subject being discussed, while the "theme" is the broader subject, the point or message that the author is trying to convey.