If you plugged in the new drive, set it up as a TimeMachine drive, and initiated the first backup this is what I’d expect. Explanation:
TimeMachine makes an initial backup and then backs up any changes on an hourly basis. That means the old drive not only has your current data but lots of old data too. Assuming you did as I described above, the new drive doesn’t have any of the old data. Just the new. Thus the discrepancy.
Solutions:
I like TimeMachine precisely because it does keep the old data. It has saved my bacon a few times over the years. You could simply retire the old TM drive to a drawer for safe keeping. Once you figure you’ve reached the point where the old data on the old drive is no longer needed you can repurpose that drive. Or, you could erase the new drive and copy the old TM drive to the new one. Apple’s official methodology is to simply drag the old TM folder onto the new drive but that can take a long long time. I prefer to use the Disk Utility restore function to perform the copy