Exactly - end over end
Well, sort of.
The barrel of most guns is rifled, that is, has a spiral cut into it so that the bullet spins around its long axis while in flight. Imagine a good forward pass in football. The pointed end always faces forward, and the body is spinning around like a top. This tends to gyroscopically stabilize the trajectory of the bullet.
However, when the bullet enters a medium with higher density, that spin rate is usually not fast enough to stop it from tumbling. Most of the mass of a bullet is near the base, rather than near the tip. So, as it travels through the higher density medium, it tends to swap ends, and travel heavy end first. This is "tumbling" as most people think of it. The motion is similar to that of a punted football.
There's a separate issue with some 5.56mm ammunition - the bullets have a groove cut around their circumference, and once it enters a higher density medium the bullet breaks apart at this groove and fragments.
All the above discussion has been for what's known as "full metal jacket" bullets. If there's a soft point or hollow point, then the bullet doesn't flip end over end after entering high density medium; instead, the jacket peels backward and the diameter increases greatly. Then one also gets all the fragmentation and tumbling and so forth.
If the bullet never enters a medium with density greater than that of air, none of this tumbling effect happens.