Rivers, streams, and creeks are a lot shallower than lakes - which means that trout can usually see movement on nearby banks. This is why experienced anglers often use care when approaching the water (so as not to startle fish).
It's also important to stay still as much as possible when fishing on the bank. Trout have a wider field of view than we do and can often see us before we see them - and our movement will chase them away.
Likewise, careless wading and walking in the water can result in overturning rocks - which in turn send a signal to trout that you're nearby. This again, will chase them out of the area.
While excessive movement can scare trout away - being still can have the opposite effect. The more safe and secure trout feel, the more likely they will be to swim into an area. This is why trout often hang around submerged logs, undercut banks, and large rocks. These structures give them shelter from predators.
So, if you want to catch trout, you'll want to look for these structures when fishing in rivers, streams and creeks and fish close to them. The next key is to be as still as possible when fishing so as not to startle fish away.
The video below does a good job of demonstrating this point. It was created by my good friend Timothy Kusherets. It's hard to see the fish swimming by him in the first two minutes of the video. But about 30 seconds more into it, the fish become much easier to see as they rise out of the water. Notice how they gradually get closer and closer to Timothy as he continues to remain still.