"Are they similar or different?" Can somebody help me with an example?
It's almost like comparing apples and oranges. There are many different types of apples, and many different types of oranges. Generalizations can be made, but specific differences will be far easier to give you if you could specify a specific version (for example: Galician or Andalusian for European, Northern Mexico or Cuban for American).
The primary difference is the pronunciation of z and c followed by e or i where in most (but not all) Spain it is realized as /θ/ and in America as /s/. Other letters such as ch, j, ll, rr, s and y may have different pronunciations but they can generally be found on both sides of the Atlantic and not necessarily in cleanly overlapping areas.
Also, in some regions, e and i can be reduced to a single vowel, ditto for o and u. I'm pretty sure that's exclusive to only some parts of American Spanish (because some indigenous languages have only three main vowels) but maybe it happens in African Spanish too due to Arabic also only having three vowels.