There is actually a difference between 探す and 捜す?
According to my online dictionary, sagasu means:
1. To search (for something lost); to seek (a suspect in a crime) — Esp. 捜す
2. To search (for something desired, needed); to look for — Esp. 探す

However, I have seen lot of examples where 捜す is used for desired things and 探す for lost things too. Also, it seems 探す (N4 word and 400 examples) is more used than 捜す (N2 word and 80 examples). That makes me think that, actually, both words have the same meaning and they are replacing 捜す with 探す since they are pronounced in the same way, making no difference in conversations.

Anyway, I would like to know the opinion of a native speaker to tell me if these verbs are really interchangeable or if there are situations where they aren't. Or any other detail I should know to avoid mistakes.

Question

There is actually a difference between 探す and 捜す?
According to my online dictionary, sagasu means:
1. To search (for something lost);  to seek (a suspect in a crime)  — Esp. 捜す
2. To search (for something desired, needed);  to look for  — Esp. 探す

However, I have seen lot of examples where 捜す is used for desired things and 探す for lost things too. Also, it seems 探す (N4 word and 400 examples) is more used than 捜す (N2 word and 80 examples). That makes me think that, actually, both words have the same meaning and they are replacing 捜す with 探す since they are pronounced in the same way, making no difference in conversations.

Anyway, I would like to know the opinion of a native speaker to tell me if these verbs are really  interchangeable or if there are situations where they aren't. Or any other detail I should know to avoid mistakes.

Answer

*** Tentative conclusion

探す and 捜す are almost same, or 99% same.
I believe 探す is more used.
I personally use 探す,or さがす when I write.

*** Japanese language has developed itself in a unique/strange way. Detailed definitions/distictions are done by Kanji, not by sound.

e.g.
The following verbs has same sound, same accent "TORU"

取る(take)
捕る(catch)
盗る(steal)
採る(pick )
獲る(get )
撮る(take a picture, shoot a film)
録る(record )
摂る(eat)
執る(execute)

The original meaning of 'とる' is "get by hand". 手（TE) and "(TO）RU" share the same root.
Though the verbs above apparently mean diffrent, they share one common concept, "doing by hand".

Same thing happen in 探す and 捜す。

Original meaning of 'SAGASU' is 'expose the thing to the sun/wind, (to find out what you want'

I don't know the difference between Chinese characters, 探 and 捜.

**** 探す(SAGASU) and 探る(SAGURU)

- The original meaning of さぐる（SAGURU）
is "touching around by fingers"

Though さぐる and さがす are diffrent words, they share the same aim of action,  "to find out what you want". Then the same Kanji”探" was applied.

Answer

By the way, same thing happen in 'はなす'

離す(let go)
放す(let go)
話す(let go -> talk)