täglich
daily
Taking place, repeating, or being available every day.
Er geht täglich eine Stunde mit seinem Hund spazieren.
He walks his dog for an hour daily.

daily
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daily
Taking place, repeating, or being available every day.
Er geht täglich eine Stunde mit seinem Hund spazieren.
He walks his dog for an hour daily.

The word 'täglich' (daily) is derived from the noun 'der Tag' (day) with the ending '-lich' (-ly/-ly-like). This structure is also found in other time expressions like 'wöchentlich' (weekly, from Woche), 'monatlich' (monthly, from Monat), and 'jährlich' (yearly, from Jahr).
Diese Zeitschrift erscheint wöchentlich.
This magazine is published weekly.
'Täglich' (daily) can stand before a noun as an adjective and is then declined. It can also be used as an adverb to describe a verb, and then it remains unchanged.
Die tägliche Dosis Nachrichten kann anstrengend sein.
The daily dose of news can be exhausting.
In the meaning 'alltäglich' (everyday), 'täglich' is often combined with nouns that describe routine or life. Common examples are 'das tägliche Leben' (daily/everyday life), 'die tägliche Routine' (daily routine), or 'tägliche Aufgaben' (daily tasks).
Das sind die kleinen Freuden des täglichen Lebens.
These are the small joys of everyday life.
day
'Tag für Tag' and 'täglich' can both mean that something happens every day. 'täglich' is short and neutral and works well for schedules, services, or habits. 'Tag für Tag' sounds a bit stronger and emphasizes repetition over several days. In their basic meaning, however, they are very similar: they refer to something that happens every day.

Die Apotheke ist täglich bis achtzehn Uhr geöffnet.
The pharmacy is open daily until six o'clock.
Tag für Tag fährt sie mit dem Bus zur Arbeit.
Day after day, she takes the bus to work.