Even if the same formulas are used, spatially and temporally dependent variables, in all settings outside of toy problems are either random or non-random approximations. The true temperature at any point in space is going to be impacted by uncountably many factors in the ambient environment. If you are laying on dry ground during a cold day, you are going to be less cold than if you are standing up straight. If you are on the roof of your house, you are going to feel colder than if you are standing in front of the house and the house is blocking the wind. There is no such thing as a “true” ambient temperature summed up in one number at a point in time, since temperature varies by space in every direction. The idea behind “feels-like” is that you are trying to capture an actual temperature value in a **typical** context for a **typical** human. How you define typical is going to itself be a parameter that can be adjusted.

What we have in such a setting is an underlying continuous distribution of temperatures and information about distributions are encoded in **expected values**, which are weighted averages of your variable of interest (or some power/combination of it, as is the case with variance [x^2 - mean of x]). So when you are modelling the temperature or anything non-trivial in nature, you are modelling expected values.

Since we cannot get every single point in space (given that space is continuous and uncountably infinite), we have to instead sample from space using things such as sensors; this introduces sampling and measurement error into an estimation of the expected value which is itself, in a sense, an approximation (more precisely, estimate) of the actual temperature you will experience outside.

Given all of the sources of error from sampling, measurement, etc. it should be expected that there will be variance in estimates how cold/hot the outside will feel. The only reason we should expect there to be consistency is if all of these places are using the exact same data sources and algorithms, and I don’t know if that would be the case. Different places, even on the same website (because how do we know the website is directly connected to the primary source?), may also have different algorithms for correcting errors even if they use the same data sources and same formulas/models.

This would be a question for @sunburntcat , who does a lot with weather data.