To suggest something means you "should" do something. To recommend something means you "could" do something.

No. Recommendation has nothing to do with whether you can do something. To restate. There is a subtle difference between the two words. Recommendations are a special kind of suggestion. They are suggestions you're saying you personally would favour. eg. I could suggest that someone jump off a cliff. I cannot recommend that. Do you see the difference? I can suggest someone eat the apple pie, but it isn't a recommendation. If I recommend it, it means I endorse that decision. It is what I personally consider the best suggestion if you like.

A recommendation is a suggestion which you personally favour.