Those thin clouds in the sky are known as airplane contrails
Some planes in the sky leave trails that persist and spread, and other planes, in the same sky, leave short-lived trails, or no trails at all.
These trails are actually called contrails, short for “condensation trails”. They are not smoke from the engines, they are formed when the water in jet exhaust (and there’s quite a lot of it, like car exhaust on a cold day) mixes with wet cold air, and condenses and freezes into ice crystals. Contrails are actually a type of cirrus cloud. When the air is wet and cold enough the trails can stay around for a long time, and sometimes spread out.
This difference between trails that fade away, and trails that spread, is often used as evidence of the “chemtrail” theory, which states that the longer lasting trails (or some of them) are being deliberately manipulated for some reason. This is not true!
Contrails can fade away, and contrails can persist and spread. It depends on the air they are formed in.There are two main reasons why some planes leave trails and some nearby planes do not. The less common reason, is that different planes have different engines. Some engines will leave a contrail in air where another engine will not.
The main reason that one plane makes contrails, or makes contrails that persist, and the other plane does not, is that they are in different regions of air. Let’s refer to these regions of air as wet air and dry air.
When the plane is in wet air, it makes a contrail. In dry air it does not. And keep in mind planes do not have to be kilometers apart because wet and dry air can exist a few meters away from each other