Is the cloud and one drive the same thing?
Yes.
"The cloud" means the internet. It's simply an expression.
Storing something "in the cloud" means storing it on the internet, instead of (or in addition to) storing it on your hard drive.
Many companies offer a cloud storage service, by which they will store your data in the cloud.
OneDrive is Microsoft's brand name for their cloud storage service, just like Google Drive is Google's brand name for their cloud storage service, and iCloud is Apple's name for their cloud storage service, and Amazon Web Services is ... you get the picture.
If you'd like to know just how these companies go about storing data 'in the cloud' I will gladly explain.