Profile pictures and pins are different jobs
People arrive at Pinterest tools wanting one of two unrelated things: someone's avatar, or the media inside a pin. This page does the first. If you want to save a video, image or GIF from a pin, use the Pinterest pin downloader instead — it takes a pin link rather than a username and is built separately, so the two never interfere with each other.
Username, not display name
A Pinterest profile shows a display name in large text, which frequently contains spaces, emoji or a business name. The username is the part in the address bar after pinterest.com/. Only that works here. Pasting the whole profile URL is fine — the username is extracted from it.
Regional domains such as pinterest.co.uk, pinterest.de and br.pinterest.com all point at the same accounts, so a link from any of them works.
Business and personal accounts
Both behave the same way for avatars. Business accounts often have sharper images simply because the picture was prepared as a logo before uploading, while personal accounts more often use a phone photo that was already compressed.
What limits the result
Pinterest stores avatars at up to 750 pixels, and does not enlarge what it receives. If someone uploaded a small image, the stored copy stays small. That is the honest ceiling; any tool claiming a much higher figure for Pinterest avatars is upscaling after the fact.