天
1, as Noun, means
1) sky; heaven:
under the open sky; in the open; 露天
sail the blue heavens 在蓝天中翱翔
2) day:
in two or three days; 过两天/日
a few days ago; 前几天/日
3) a period of time in a day:
It's still early. 天儿还早呢。
4) season:
summer; 夏天
winter; 冬天
5) weather:
overcast; cloudy day; 阴天
wet weather; 雨天
2, as Measure word, means
1) day
一天, one day
两天, two days
三天, three days
日
1, as Noun
1) sun:
the rising [morning] sun; 旭日
2) daytime; day:
day and night; night and day; 日日夜夜
In summer the days are long and the nights short. 夏季日长夜短。
3) day:
today; 今日
Haven't seen you for a long time. How are you? 多日/天不见了， 你好吗?
4) time:
springtime; spring; 春日/天
the days to come; the future; 来日
天 VS 日
天 used in oral, 日 used in writing
一天 / 一日 one day （OK）
两天 / 两日 two days （OK）
今天 / 今日 today （OK）
星期天 / 星期日 the Sunday（OK）
签证两个工作日以后来取。（OK）
签证两个工作天来取。（NOK)
你的生日是几月几日？（OK）
你的生天是几月几天？(NOK)
天, 日, 号 are all used to express time, the differences here:
1) 天 vs 日
To count days, put the number right before the word for the day. No additional classifier is used:
一天/日, one day
二天/日, two days
To ask about the number of days, say:
几天/日? How many days? (small number expected)
需要几天/日？How long does it take?
Referring to days before and after today
前天, the day before yesterday
昨天, yesterday
今天, today
明天, tomorrow
后天, the day after tomorrow
2) 天 vs 号
There are two words for a date that are used when referring to the date of the month, 号 and 日. 日 is more formal than 号 and is used in calendars and other written documents.
To indicate the date, put the number directly before 日 or 号:
5 号/日, the 5th of the month
22 号/日, the 22nd of the month
To ask about the date, say:
几号/日: What is the date?
今天几号？What is today's date?
今天几日？(don't say like this!)