Later and next time
These push something to a later point: later today, the next occasion, next in line, or again.
mata
again
また
Says something happens again (mata kita), and closes goodbyes and invitations (mata ne, mata kite ne).
mata watashi ga harau no?
I'm paying again?
また私が払うの？
mata watashi ga harau n desu ka?
I'm paying again?
また私が払うんですか？
mata ne and mata ashita are the everyday goodbyes. The 'also' sense belongs to connectors. Men say ore here in casual talk (mata ore ga harau no?).
ato de
later
後で あとで
Puts something off until later, usually the same day (ato de ne). After a -ta verb, -ta ato de means 'after doing'.
ato de harau ne.
I'll pay you later.
後で払うね。
ato de haraimasu ne.
I'll pay you later.
後で払いますね。
Business speech uses nochi hodo. ato de is fine in ordinary polite talk. ato + an amount means 'X more, X left' (ato go-fun = five more minutes).
kondo
next time; this time; sometime
今度 こんど
Points to the next occasion or some future one. It is how people float plans and soft invitations (kondo nomi ni ikou).
kondo harau ne.
I'll pay next time.
今度払うね。
kondo haraimasu ne.
I'll pay next time.
今度払いますね。
mata kondo ('another time') is often a polite no. kondo no + a day means 'this coming' (kondo no doyoubi). After an earlier try, kondo wa can mean 'this time' (kondo wa umaku itta).
tsugi
next
次 つぎ
Points to the next item in a sequence or line (tsugi no eki, tsugi wa?). tsugi ni marks the next step.
tsugi doko iku?
Where to next?
次どこ行く？
tsugi wa doko ni ikimasu ka?
Where to next?
次はどこに行きますか？
tsugi wa also means 'next time' for a definite next occurrence (tsugi wa ki o tsukete = be careful next time). kondo is vaguer and is the word for invitations.