Salute/səˈluːt/ and Greet /ɡriːt/ are two verbs that both mean "hello, welcome, welcome", however used in different contexts.

Salute:

 To touch the side of your head with the fingers of your right hand to show respect, especially in the armed forces.

This means putting the right hand on the forehead, placing a thumb in 45-degree contact with the forehead that represents a formal greeting, especially for use in the military.

Ex. The sergeant stood to attention and saluted. The sergeants stood solemnly and saluted.

To express respect and admiration for somebody/something. Show respect and admiration for someone, something.

Ex. The players saluted the fans before leaving the field. These players greeted their fans before leaving the pitch.

Hello, hello to someone.

Ex. She greeted us with a smile. She greeted us with a smile.

React to someone, something in a special way.

Ex. The team's win was greeted as a major triumph. The team's victory was celebrated as a great joy.

Ex. When she opened the door she was greeted by a scene of utter confusion. When she opened the door, everyone was greeted by a loud cheer.

Reference material: English Usage for Learner & Oxford Advanced Learner's Dictionary. Compiled by teacher of SGV Foreign Language Center.