Photoshop
GIF - Graphics Interlaced File: Small files that can compress easily, they take up little to no size, originally made 29 years ago but GIF files can lose detail for print or saving.
JPEG - Joint Photographic Experts Group: Quality is quite decent, can be printed or used for web can be sent to other softwares.
PNG - Portable Network Graphics: Quality is excellent, if there was a white background then the PNG will read this as a transparent background.
TIFF - Tagged Image File Format: Excellent quality, however the downside to this is it can't be compressed.
PDF - Portable Document Format: You can save microsoft and photoshop documents as a PDF file. Has it's own version, can't edit any text or use any layers and is ONLY for print.
EPS -
Adobe Illustrator
SVG - Scalable Vector Graphics: Design to be seen on-screen, and it is only used for web.
AI - Adobe Illustrator: