Smoke after cooking = grease?
Scientifically speaking, smoke is a solid mixed with a gas, so no, smoke is not grease.

However, the smoke that gets generated by the decomposition of cooking oils (called the "smoke point") at a certain temperature (T°) is mixed with grease molecules and yes, they settle down somewhere.  

To explain further let's take an analogy with water at 1 ATM


1L of water boils at 100°C
At 75°C it evaporates rather quickly
at 50°C it evaporates quicker than at room T°
at 25°C it will eventually evaporate (Room T°)
at 0°C it will sublimate rather slowly


Now, with cooking oils, the smoke point is way below the boiling point for most, but as you can see from the above analogy they will evaporate though more slowly than water as an oil molecule is heavier so takes more energy to get "kicked" out of the liquid.

Note 1: I tried finding a list of cooking oils with both their boiling and smoke points but couldn't find a decent list with both, but it's irrelevant to the question as any liquid does evaporate at room T° eventually...
Note 2: The best way to ensure the grease molecules don't settle down inside is to ensure there is excellent ventilation or invest in a high-volume extractor