What is the difference between "~ masu" and "~ te imasu"?
The suffix "~ masu （～ます）" is the present tense of a verb. It is used in formal situations.

Ongaku o kikimasu. - I listen music.
Hon o yomimasu. - I read a book.

When "~ imasu （～います）" follows the "te form" of a verb, it describes progressive, habitual or condition. 
a)It indicates that an action is ongoing. It is translated as the "~ ing" of English verbs. 

Denwa o shite imasu. - I am making a phone call.
Shigoto o sagashite imasu. - I am looking for a job


b)It indicates repeated actions or constant states. 
Eigo o oshiete imasu. - I teach English.
Nihon ni sunde imasu. - i live in japan


c)It describes a condition, situation or the result of an action.
Kekkon shite imasu. - I am married
Megane o kakete imasu. - I wear glasses
Mado ga shimatte imasu. - the window is closed