The differences are subtle, very subtle. First though, recognize the difference in two words, "adviCe" and "adviSe". Advice is a noun, advise is a verb. Suggest and recommend are both verbs. So, as a group of verbs we have suggest, recommend and advise. The related group of nouns is suggestion, recommendation and advice. Here are the subtle differences: a suggestion is not as strong as a recommendation. Advice is stronger than a recommendation. A suggestion can be stated as "Well, given what you have said, I think you should do this." A recommendation can be stated as "Given what you have said, my recommendation is to do this." And advice can be stated as "Based on my expereince, in your circumstance, my advice to you is this." People use them interchangeably even though there are differences. One last note, when you are talking to a professional (doctor, lawyer, accountant, engineer, architect, etc.) about what they think you should do, they offer you their "professional advice" or "professional opinion". It is based on training and experience and is therefore usually much more reliable than the recommendations or suggestions of others.

They have meanings that partially overlap. That means that in some contexts they are interchangeable but in some they aren't. For example, I might suggest or recommend a good restaurant; I'd advise you against eating at a bad one. In this context, suggest and recommend have similar meanings (though 'recommend' suggests I've been there before). "Advise" is stronger. If there are two restaurants, one good and one bad, I'd advise you to go to the good one. I would think it a mistake if you didn't take my advice.