Yes, they are synonyms, and you can use any of them in many situations. For example, "I'm worried about you" in Russian is either "Я беспокоюсь о тебе" or "Я волнуюсь за тебя".

I. From "волна", 'wave'. This image of a wavy surface (and your mind carried by waves), it is important. Волновать - cause waves on a surface (rare) - cause a range of emotions, from "worries" to sexual arousal. "меня волнует [some fact]" - this fact disturbs me "эта новость взволновала меня" - concern, worries or excitement - any strong feeling "не надо его зря волновать" - don't make him feel strong emotions without a reason. "меня волнует вот такой вопрос:..." - the speaker can literally mean emotions/concerns... or he can just ironically mean: "i wonder/I'm curious". Меня не волнует! "i don't care! I'm indifferent to this!" Cf.: Меня это не беспокоит. It doesn't disturb/bother me, I don't find it a reason for concern Я не волнуюсь! No, I'm not worried/emotional! Волнительный, adj. - classic Russian literature, mostly positive. Causing strong emotions. Including romantic feelings. Волнующий - more straightforward grammatically, 'making wavy', 'causing волнение'. -- participle: волнующая меня новость - новость, которая волнует меня. -- adjective: волнующая новость (worrying or exciting or...) волнующие движения (an erotic example: someone feels things observing other person's movements) Волноваться 1. About a sea (море волнуется, волнение на море): there are waves/storm. 2. Without "за". Can mean the same as with "за" (я волнуюсь!), but not only. An actor may feel this before public performance, or a guy/girl before a date. It does not necessary mean 'fear of failure', and it doesn't mean at all any specific concern about a particular failure! It jsut means: your emotions affect you. 3. Волноваться за someone/something. To worry for... , to worry about...

I agree with Евгений. In "I'm worried about someone" and in other situations when your emotional state is KNOWN to us, they are the same. We know what exactly you feel and we imagine this emotion. We don't think at all about 'shades' and other meanings, we foucs on the meaning of your message:) Otherwise, when there is a range of possible emotions/feelings, and the word is used to describe/specify, they aren't the same. Moreover, they have meanings the other word doesn't have. I'll describe them in separate entries.

in most situations it is sinonyms. if it is just "i am worried", doesnt matter what you say. but in some situations you cant say different. like "restless" it is беспокойный, if you say волнительный it means exhilarating. Беспокоиться more means that you worry about it. You can "волноваться" thinking about beautiful moments in your life. its a broader concept. hope im rights))

II. Беспокоиться. "without" (без) and "rest". Беспокоить - (figuratively) to disturb. Не надо его зря беспокоить. (he a busy man, don't disturb him with problems that don't worth it) - to cause unease, to make worry, concerned (all negative emotions related to concerns) Что-то меня беспокоит.... Something keeps bothering me.. I'm not quite sure what. Меня беспокоит задержка с оплатой:-/ Беспокойный - adjective, - restless (e.g. your roomate:)) - nervous Беcпокоиться - to feel concerned/worried about something. Often thinking about a specific problem/danger. Беспокоиться за... Close to "волноваться за..." or "worry for..."