Hello Alex! I hope these information can be useful.
First, it's interesting to take a look at the most common definations for these words according to the dictionary.
- verb CONHECER
1) to know, have a notion of, to perceive, understand
2) to be familiar with
3) to be acquainted with, meet
Examples
- Meaning 1: "Eu conheço trigonometria." (I know trigonometry)
- Meaning 2: "Eu conheço o Alex muito bem." (I know Alex very well)
- Meaning 4: "Prazer em conhecê-lo!" (Nice to meet you!)
- verb SABER:
1) to know, have information about (= conhecer)
2) to have practical knowledge of, be skilled in
3) (used as a noun) knowledge, learning, erudition, wisdom
Examples
- Meaning 1: "Eu sei sobre trigonometria." (I know trigonometry)
- Meaning 2: "Você sabe falar inglês?" (Can you speak english?)
- Meaning 3: "O saber resolve casos como este." (The knowledge can solve cases like this)
You can see that they have very similar meanings but they are not always interchangeable, even when majority of translators point the English verb "to know" for both.
I think that the 2 biggest differences are:
-> When you need to express the idea of "meet" or "be familiar with", in Portuguese only the verb "CONHECER" is used.
-> When you need to express the idea of "be able to do something" or "be skilled in", in Portuguese usually the verb "SABER" is used.
In the other situations, usually you can use both.
... Remember I said "usually" :-)