One means 'to encircle, surround' the other means 'to enclose'. I am having trouble figuring out which is used when, had a look at one example sentence for each but still not clear since the >difference< between the two is not being exclusively explained.

Are you coming up with these by starting with kanji and looking at the verbs that are written with them? I think that's naturally going to get you a lot of confusing synonyms and near-synonyms. My suggestion would be to pick the words you look at based on what you actually read/encounter (in textbooks, in real life, in vaguely frequency sorted word lists), which will tend to mean you get the common option first, and by the time you encounter other synonyms you'll at least have a reasonable grasp of half of the pair. In this case my experience is that 囲む is the way more common of the two.

(I hadn't actually (conciously) encountered 囲う before this post, in fact. A little checking with dictionaries suggests that it's more specifically about the idea of setting up a boundary between the inside and the outside, eg: 警官は、現場の近くをロープで囲った。 The police roped off the street near the spot. 囲む is I think broader in meaning, you can use it to talk about towns being surrounded by mountains or people sitting around a fire.)

If you're okay with Japanese explanations, another way to search is to try Googling various terms to find some language Q&A sites:
eg ”囲む”　"囲う”　"違い”
”囲む”　"囲う”　grammar, etc

The quality of answers is hit and miss, but they might more detail than a regular dictionary. Here's one eg: http://oshiete.goo.ne.jp/qa/6517233.html (note that the first response misunderstood part of the question)

This JOI lesson has E and J:
http://joi-japonin.blogspot.com/2010/11/...verbs.html
(I wonder if the JOI teacher meant that kept mistresses have become less common in Japan or that using 囲う　for that meaning is less common. haha It seems to convey "secretly hidden", but sounds more like "caged/enclosed" to me. Especially if it's also used for criminals...)

Those answers confirm pm215's interpretation that 囲う　is used more often when the purpose and method are important (rope off, wrap to protect, etc.) It's focus is more on what's being enclosed/separated. It's more common with things they say, but can be used for people.

囲む is described as being more about the act of surrounding - something is encircled by ~. (Often passive.) It's used for both people and things. Unlike　囲う, however, when the enclosed is a thing, 囲む is not really about purpose.

I bet you'll find lots of overlap and other subtle nuances, though, so I wouldn't aim for precise distinctions. As pm215 says, by reading you'll get a feel for common usage.

thanks dudes , so are these words called 類語?