A mean and a covariance instead of a cloud
Where a particle filter represents belief as thousands of discrete samples, a Kalman filter represents it as a single mathematical object: a Gaussian, a bell-curve-shaped distribution defined by just two things, a mean, the best-estimate position, and a covariance, a measure of how spread out, and how correlated across dimensions, the uncertainty around that estimate is. Instead of simulating many possible positions, the filter directly updates these two quantities using closed-form equations.
The predict step shifts the mean forward according to the motion command and grows the covariance to reflect the added uncertainty from imprecise motion, exactly the same conceptual move as in a particle filter, just expressed algebraically instead of by moving particles. The update step then combines this predicted belief with a new sensor reading using a weighting factor, commonly called the Kalman gain, that automatically balances how much to trust the prediction versus how much to trust the new measurement, based on how uncertain each one currently is.