There is no good answer to this.
Functionally, conceptually-- the amount of region any given sort of giant would need to control, the amount of resources any single one would need to live... It just isn't possible for any single tribe to have a particularly significant population. And I have never seen a D&D world that has actually given them the kind of space they would need. Its always like "yeah, there are about 15 or so giants in those mountains and the leader is called a king". And it is usually in terrain that wouldn't produce enough to feed and cloth them no less!
So given how small any given giant tribe is, one would think that unless they are so inbred that a whole lot of negative recessive traits are going to start showing up across their whole populous... well, obviously they need to be interbreeding with other tribes.
But, at the same time, there is significant difference between each type of giant that it is absolutely impossible that the various types are interbreeding. You just couldn't be so specialized for each environment without having absolutely divided genetic pools for thousands of generations.
The reality is just that... D&D has never been designed to be any sort of rational, functional, properly built world that is at all sensibly put together. It is simply about "here is your bag of hit points to pop at your particular level" and the hierarchy of giants or dragons or anything else is just... well... what level the original people who used that monster concept decided to throw them at the PCs to be slaughtered on mass and spew out their XP and GP for players to collect.
If you wanted a world that is actually built in such a way that anything makes any sense at all and it isn't just "hey, random monster appears in room 36 because that's what I rolled out of the entire possible monster manual of creatures of your level to appear in this room and there is no story for why it is here, it literally just poofed into existence because you opened a door to this room and it is absolutely in no way connected to any of the other randomly generated monsters that will appear when you open the doors to the adjacent rooms."
In the case of giants, it was just that some random person at some random time decided that players would be popping bags of hit points for their XP/GP rewards at level X and the giants at that level would be called "_____ giant", generally neatly fitting in the general elements because that was an easy way to differentiate one from the next. One had to call them something after all.
Once you are trying to make a world that well... works... on any kind of rationally-satisfying level, you cannot simultaneously hold to the exact stat blocks given in the monster manual as though they are unquestionable holy gospel.
By all means you could have a cloud giant that is a much better warrior than your typical storm giant. If it is even conceptual that you can ever have a human who could possibly take down a giant in melee combat (something that is plenty possible!) then there is absolutely no reason whatsoever that the creatures in the monster manual, certainly those that are sentient and born and grow and have experiences, would be absolutely eternally stuck with only that particularly proscribed stat block and utterly incapable of changing or improving or advancing in any manner.
The stat blocks are just there to give you an easy thing to toss out for the express purpose of having PCs beat on them like different sized pinatas that can hit back. The moment you have infused any personality, any thought, any motivation, any character into the concept... you have violated the purpose those stat blocks are there to serve and now they are simply loose guidelines that you can use as a starter.
In your particular situation there, rather than what the stat blocks read-- there is a deeper question at stake.
If intermarrying were common or even uncommon but happened often enough that one were as likely to find a mixed blood as not... why are there even "Cloud Giants" and "Storm Giants" as separately label-able things? What exactly is it that is keeping these groups as separate breeding pools? A clear answer to this is not going to be in the book. Nor is anyone going to have the definitive answer for you. You are going to have to come up with that answer yourself.
And once you decide what the answer is, you are going to have to decide yourself what it would take to violate it. Or if it is even worth violating. Because, as I already wrote, if Cloud Giants are a separate and rival tribe to Storm Giants, there is no reason they cannot train and arm and level up and raise a badass enough military to come and beat the Storm Giants down. It is no different than humans rising up to take on hobgoblins or draconians.