The thing is, most (or most) of the hosting providers out there that has DDoS Prot have their clients share all the DDoS Protection. Thay's why we are seeing some claims they have Terabytes of DDos Protections and such. Do custom ones is still possible.
About being specific to OVH, OVH does have 2 kinds of DDoS Prot ( as for my knowledge) it is the Basic DDoS Protection and Game Server DDoS Protections. The difference in my opinion is Game Server DDoS Prot by OVH is more optimized for games especially TCP ones.
And yeah. Both can house a website as long as you have the resources to do so. Websites doesn't take ton of resources unless you are getting massive visits.
For reference:
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