It's all to do with the dominant and recessive genes. When it says rare, the gene is mutated. For example, a red tulip gene and a white tulip gene will mutate into a pink/white tulip 70% of the time. Say you bred two orange tulips and got a pink, that would mean that one of those oranges had a recessive pink gene. This isnt a mutation: the gene was already there. You just couldnt see it.
Is there a difference? Not really, no. The main thing is you can be certain of the genealogy of a mutated seed.
It all depends how interested you are in the gardening mechanic in general. If youre not that bothered, a rare seed compared to another seed of the same colour means pretty much nothing. If youre quite into it, it'll tell you where it came from and what its gene make up is. Ironically, if you're into it, you probably didnt need it to tell you anyway.
Take the breeding of an orange/white tulip (the kind Lloid gives) and a black/white tulip (which is the make-up of a mutated "rare" black seed). All genes have a 50% chance of inheriting, and a white/white combination has a 70% chance of mutating into a black/white "rare" seed. A tulip will always show up as whatever gene it has which is higher on the dominance scale. In this case, all we need to know is that orange beats black, and black beat white. The resulting seed will have these odds:
Orange/black - an orange tulip with a black recessive gene. 25% chance.
Orange/white - orange tulip with white recessive. 25% chance.
White/black - a black tulip with a white recessive. 25% chance. Will not be tagged as rare as it isnt a mutation, just a dominant black gene.
White/white - a purebred white tulip. 7.5% chance. (30% of 25% - the chance of a white/white combination not mutating)
Black/white - a mutated black tulip. All mutated blacks have this gene combo. 17.5% chance (70% chance of getting correct combination and it mutating). This seed, unlike the other black tulip you could get from this combination, will be marked as rare, despite it being genetically identical to the former now.
So in actuality this combination gives a 42.5% (25+17.5) chance of giving a black tulip. Some will be marked as rare and some wont, but they will all be genetically identical.
Check these pages out for full information on how flower breeding works.
Guide for Tulips
Guide for Pansies
And feel free to ask anything too. Im not infallible but I get it pretty well I think.