温存 and 保存
Which basically means "保存する preciously". So if we look at the other one, we should get both meanings, right?
Which means "conserve it in its current state".
The main translation we get for 温存 is "preserve" which makes sense because if we look up "preserve" in the dictionary, we get:
to keep something as it is, especially in order to prevent it from decaying or being damaged or destroyed
Which is quite similar to the one we get for 温存 on https://dictionary.goo.ne.jp/thsrs/1927/meaning/m0u/
【２】「温存」は、消耗をさけ、力を残しておくこと。 Which basically means to keep something so that it doesn't get 消耗 and keeps its 力.
We can also kind of get the same meaning from the kanji:
温 : temperature
存 : save
For 保存 now, the main meaning we get is "conservation" which, if we look up in the dictionary, means:
to keep and protect something from damage, change, or waste
So here again, that's pretty close to the meaning we get on goo.ne, which is:
【１】「保存」は、いたみやすいもの、なくなりやすいものをそのままの状態に保っておくこと。 : keep something that is easily breakable or "loseable" in its current state
Let's look at the kanji now:
To sum it up for these two words, we can see that 保存 can be seen as a "neutral" version of 温存, which means to keep something so that its state doesn't change. Whereas 温存 means to keep something so that its state doesn't change (especially doesn't get bad).
詮索 and 検索 and 探索
詮索: ［名］(スル)細かい点まで調べ求めること。https://kotobank.jp/word/%E8%A9%AE%E7%B4%A2-549979 : Search until small points (details)
検索: ［名］(スル)調べて探しだすこと。https://dictionary.goo.ne.jp/jn/69682/meaning/m0u/%E6%A4%9C%E7%B4%A2/ : find out by searching
探索: 未知の事柄などをさぐり調べること。 https://dictionary.goo.ne.jp/jn/139943/meaning/m0u/%E6%8E%A2%E7%B4%A2/ : research unknown events
We can see that this word has a rather negative meaning, and "pry" is the meaning we find the most:
And it's quite similar to the Japanese meaning, so I think we can put pry and 詮索 in the same category.
We can confirm that by looking for use examples on google 詮索, a lot of what we find is about the psychology of people who like to "詮索" (pry) or "詮索" (pry) too much.
This word seems to have a quite neutral meaning, and the 3 verbs that appear the most are "look up, search, retrieve (or locate)". Also, as you already know, it's used when we look up something in the dictionary, for example.
And as we can see on goo.ne:
【３】「検索」は、特に、書物の中にある記述を探し求める場合に用いる。 : Used in cases where you search for something in a text/book etc.
So we can think of it as "look up in order to retrieve data".
This one, too, looks quite neutral from the examples, and doesn't seem very different from 検索.
But if we look at this:
【３】「探索」は、物のありかや人の行方などを探り求めることをいう。 : Search for someone's actions/the state of something
It sounds like 探索 is more about doing the research, trying to collect data about something/someone, whereas 検索 is more about looking up already existing data, to try to retrieve it, so it makes sense that 検索 is the one used when trying to find something on the internet.
So maybe we can attribute the English "to seach for" to the word 探索, and the English "to look up" to the word 検索.