Adaptive Filters are called "Adaptive" when they can adapt to changes in data.
In the filters you mentioned above, which are part of the Linear Filters family the property means their coefficients are changing over time.
Linear Filters are basically weighing and summing the data.
For instance, given no prior information on data you may want to have exact weight for any data given.
Yet in most Signal Processing use cases we'd like to (Or might want to) give higher weight for each data sample according to its properties such as SNR, How good it fit the model, etc...
In the classic Kalman Filter the coefficients are set according to a model matrix - $ P $.
For Kalman filter this matrix stands for the Covariance of the estimation.
It changes according to 2 other matrices which are properties of our model and data - $ Q $ - The model confidence level matrix, $ R $ the data confidence model (For Gaussian data it is basically the SNR).
Since the algorithm support the cases those are changing over time it is called adaptive.
For instance, in the case of tracking a target using RADAR the algorithm can change the matrix $ R $ according to the SNR of the measurement.
The Recursive Least Squares have similar properties (Though it depends only on one factor, something similar to the matrix $ R $ of the Kalman Filter).
One could even see the RLS as a private case of the Kalman Filter (Or the Kalman Filter as a generalization).
There are many extension for the Kalman Filter for many cases.
The UKF (Unscented Kalman Filter) you mentioned is built to handle Non Linear cases of the Model.
But adaptive concept stays the same, the weights are changing according to properties of the Data and the Model.