Blue velvet and blue dream are a blue variant 0f cherry shrimps, Neocaridina davidi. One on-line shop says that blue dream and blue velvet are the same shrimp just different names. And that they are a deep blue. They also sell blue jellies which are paler.
Royal blue would seem to be a colour variant of tiger shrimp, Caridina cantonensis.
I have never heard of gummy blue, and all google throws up are sweets.
As far as keeping them goes, velvet/dream have the same requirements as red cherry shrimps, and royal blue need the same as tiger shrimps.
Some sites say blue dream and blue velvet are the same shrimp, just different names in different places. Even if they are slightly different, they can be kept together. Their offspring will still be blue, just a blend of the two. It's different coloured shrimps that produce brown offspring, which is why red, blue, yellow and orange Neocaridina davidi should be kept separately.
Wild cherry shrimps (Neocaridina davidi) are brown. All the coloured varieties have been produced form the wild form by selective breeding. But let two different colours breed together and they revert to wild colour.
Different named variants of the same colour can be kept in the same tank. Their offspring will be the same colour. But any differences will be blended together. For example, keeping a pale blue variety with a dark blue variety will result in some pale blue offspring, some dark blue offspring and some medium blue offspring. And solid blue kept with stripey blue will produce some solid, some stripey and some with faint stripes.
If you don't mind this blending, then you can keep different blue ones together, but if you want to keep them 'pure' keep only one variety.
I've only had cherry shrimps (red ones) and amano shrimps. Blue dream and blue velvet are both blue cherry shrimps. Royal blue are tiger shrimps, but I've never kept that species. You need to research the needs of the two species to see if they can be kept together (eg do they need the same hardness, temperature etc). If they can, royal blue cannot interbreed with velvet or dream as they are in different genuses.