They don't have to be.
Mottoes can be in quotation, but they are usually in Italic.
Quotations should fit into sentences:contextually.grammatically.
According to The Oxford Dictionary for Writers and Editors, plural of motto is mottoes.
The title of a website should be underlined Italic or normal, not in quotations.
no they should not
I do not collect mottoes so I did not notice any differences.
You should not use quotations when you are paraphrasing information or providing your own analysis or commentary. Additionally, avoid using quotations for common knowledge or well-known facts that do not require attribution.
mottoes
Use quotations in your draft because they lend validity and immediacy to the writing.
The action you should never take when selecting quotations is judging them by the cost. You should consider other factors and not assume all cheap quotations are poor in quality and the expensive ones are of superior quality.
Ferruccio Rizzatti has written: 'La cultura scientifica' -- subject(s): Science, History 'Quis? Quando? Dati e date' -- subject(s): Chronology, Encyclopaedias, Inventions, Quotations, Mottoes, Tables and date books
For now it's time to explore
Quotations should go after the period at the end of the sentence when copying a sentence from a book.