In my case, they usually feel very different, like images have much more definition and places are as they are in waking life, although this varies according to the type of omen they are about . Anyway, I think that the difference may vary from person to person too, so you should probably analyse your dreams and find patterns in those that had been proved to be prophetic in order to recognize the next one.
With me, my dreams become very vivid and real. If I have dream logic within a dream (you know, where you can fly and walk through walls), I look for the presence of my guardian spirits. Dreams will have a vivid but dictated feel to them then, as if someone's been telling me what to dream.
The conscious mind mostly remembers things which are deemed important. Since on most cases dreams are a matter of the subconscious mind working out memories, small problems, re-filing different things, and sometimes just the hypocampus randomly firing off different tropes and memory elements, the brain does not consider dreams very important.
Starting a dream diary will give you a conscious intent that dreams are becoming important. Even recording that you do not remember your dreams puts into the forefront of your conscious that your dreams are more important. Before long, you will better remember your dreams.
Reoccurring dreams can be one of three things in my experience(I get prophetic dreams)
1 your subconscious mind is telling you something is wrong and you need to face it.
2 this is a possible future for yourself and your subconsciously trying to avoid the path/ or be ready for it.
3 it is an event yet to happen that will shake the very world by it happening on either a minor or major scale yet to be determined.
For example when big events happen around the world I will dream of it the night before it happens, or if it has tremendous force I'll dream of it days, weeks, months or even years in advance for a few times but it is hard to say without knowing the dream itself.