to add / to attach
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to add
To add something to something already existing, especially in writing or speech. Synonymous with 'hinzufügen' (to add).
Ich möchte noch anfügen, dass die Frist morgen abläuft.
I would still like to add that the deadline expires tomorrow.
'Anfügen' (to add/to attach) is a separable verb. The prefix 'an-' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er fügte seiner E-Mail noch ein Foto an.
He also attached a photo to his email.
You can tell whether 'anfügen' (to add/to attach) means adding information or attaching a file from the object: you add a remark (information), but attach a PDF file (document).
Lassen Sie mich noch eine kurze Bemerkung anfügen.
Let me add one brief remark.
The formulation 'Ich möchte [noch] anfügen, dass ...' (I would [still] like to add that ...) is a polite and common way to introduce additional information in a conversation or presentation.
Ich möchte noch anfügen, dass wir uns nächste Woche wieder treffen.
I would still like to add that we will meet again next week.
In the reflexive form 'sich anfügen', the verb means that something fits exactly. It is often used with the preposition 'an (+ accusative)'.
Der neue Flügel des Gebäudes fügt sich harmonisch an den Altbau an.
The new wing of the building fits harmoniously onto the old building.
to fit / suit / pass
'passen' and 'sich anfügen' can both express that something fits well with something else. 'passen' is more general and is used in many everyday situations, for example with colors, appointments, or ideas. 'sich anfügen' means more specifically that something connects harmoniously to something already existing and does not disrupt it. The word sounds somewhat more formal and is especially suitable for texts, shapes, parts, or processes. Put simply: 'passen' says that something works or fits; 'sich anfügen' says that it fits well into a whole.
Der letzte Absatz fügt sich gut an den Rest des Textes an.
The last paragraph fits well with the rest of the text.
Der neue Tisch passt gut in die kleine Küche.
The new table fits well in the small kitchen.