In this mechanism step water is a Lewis base (a nucleophile) because it is sharing an electron pair with the tert-butyl carbocation. This is an example of a Lewis base which is not a Bronsted base.
In this mechanism step water is a Lewis base (a nucleophile) because it is sharing an electron pair with the oxonium ion. Water is also a Bronsted base because it is deprotonating the oxonium ion.