Vector graphics are drawn in paths, which allows the designer to resize images freely without getting pixelated edges as is the case with bitmapped images (such as jpegs, tiff’s and eps’s). Vector format is generally used in printing while bitmap format is used for on-screen display. Vector formats are commonly supplied in Eps, Illustrator (.ai) and CorelDraw (.cd).
So, if you are required to supply a VECTOR logo, then ai, eps and pdf are the files you would select.

JPG (or JPEG) is a raster image and can be optimised to find the perfect balance of file size and quality. On the web, you want your images files to be as small as they can be so your site loads quickly, but large enough to still appear crisp and not pixelated. A JPG can not have a transparent background.

PNG is another raster image type. The main difference to understand between a PNG and JPG is that a PNG can have a transparent background and is generally larger and higher quality. PNG is ideal for saving logo files for websites because they can be placed over a coloured background.

An AI file is a proprietary, vector file type created by Adobe that is created or edited with Adobe Illustrator. It is most commonly used for creating logos, illustrations and print layouts.

An EPS file is a vector file of a graphic, text or illustration. Because in most cases it is vector it can easily be resized without compromising quality. An EPS file can be reopened and edited.

A PDF is generally a vector file. However, depending on how a PDF is originally created, it can be either a vector or a raster file. PDF files are especially useful for documents such as magazine articles, product brochures, or flyers that need to preserve the original graphic appearance online.
The A and B series of ISO 216, including the commonly used A4 size, are the international standard used. Successive paper sizes in the series A1, A2, A3, and so forth, are defined by halving the preceding paper size across the larger dimension. This also effectively halves the area of each sheet.*
SOURCE: https://enviragallery.com/whats-the-best-image-format-different-file-formats-their-features/ and https://modassicmarketing.com/understanding-image-file-types / *https://en.wikipedia.org/wiki/Paper_size
841 x 1189 mm
33.1 x 46.8 in
594 x 841 mm
23.4 x 33.1 in
420 x 594 mm
16.5 x 23.4 in
297 x 420 mm
11.7 x 16.5 in
210 x 297 mm
8.3 x 11.7 in
148 x 210 mm
5.8 x 8.3 in
105 x 148 mm
4.1 x 5.8 in
74 x 105 mm
2.9 x 4.1 in
99 x 210 mm
A4 divided into 3