Now I got it :)
The day version is simple, because the difference between two dates returns the number of days as integer: date1 - date2
Similar for adding/subtracting days: date1 + 4
Regarding timestamps it's more difficult, Teradata implemented Standard SQL syntax, but introduced some stupid limits :(
The difference between two Timestamps is an INTERVAL:
Timestamp1- Timestamp2 YEAR (similar result to DATEDIFF(year))
The default number of digits based on Standard SQL is two (up to 99 years), but it can be changed using YEAR(n), but n is limited to 4 in Teradata:
Timestamp1- Timestamp2 YEAR(4)
This is ok for years, because Teradata covers a date range 0001-01-01 to 9999-12-31, but fails soon when you calculate months/days/hours/minutes/seconds.
You can calculate complex intervals like YEAR TO MONTH or DAY TO SECOND but not across month/day.
If the difference might be more than 9999 days (= 27 years) you can go for a UDF like the one found in this thread: