The variety of different file formats for design can sometimes be a bit overwhelming, and while some have little practical difference between them, choosing which one you need will depend on your resources and requirements.
Raster or rasterised files are made of pixels, the little dots that make up the images on your screen. Think of them like putting a permanent pen mark down on a bit of paper - you can edit them but only by laying on some colour or erasing them and drawing again. Digital photos are raster images.
If you enlarge a rasterised image then the pixels will also enlarge, making it start to look blocky and fuzzy (showing "jaggies").
This is where resolution comes in to it - dots per inch (dpi). The higher the resolution, the more dots are packed into an area when it comes to print, and the higher the quality will be. Once you get above 300 dpi it won't make much difference - but higher resolutions can be useful if you want to enlarge the art (make it bigger and lower the resolution and you can keep the quality).
Vector images are mathematical shapes that can be edited and reshaped at any time. They are also independent of pixels when it comes to printing, so they can be resized up or down without losing any quality.
Raster images are file formats such as JPG, PNG and TIFF, while vector images exist in file formats such as EPS and SVG. Sometimes both can exist together, for instance in a PDF document.
Raster images will be used for photos and painted art, images that require a lot of variation in colour. Vector is best for simple graphics such as logos, titles and text.
RGB stands for red-blue-green and it is the format your computer screen (and your television) use to show colour - it is colour made of light. If you mix the RGB values together they will make white. It offers a huge variety of colours, some of which can't be printed.
CMYK stands for cyan-magenta-yellow-key - they key means black. They are basically print inks and it is the file format used for printing. If you mix the CMY colour values together they darken and make black (ish).
You will nearly always want your print files to be CMYK - if you supply RGB files, although the file size will be smaller, the colours might shift in order to become printable. If you need to supply an RGB file for print you should make sure all the colours are within the CMYK range (this can be called “in gamut”).
JPG ("jay-peg") is one of the most common file formats, and while it was created to keep image files smaller for digital use, it is often perfectly fine for printing decent quality graphics for print. JPGs can be saved at different qualities - a lower quality will result in a smaller file size but can look poor - for print the quality must be kept high.
PNG ("ping") is a high-quality raster format that has the advantage of allowing transparency, so it's great for supplying graphics that you might need to lay over a background. They can only be supplied as RGB but can be used in the layout phase before the final file is converted to a CMYK format for print.
TIFF is a high-quality raster format that can also deal with transparency, though the file sizes are usually very big compared to other formats. They are best for when you really need to keep a lot of high quality detail.
PSD (Photoshop Document) is a file format specifically for use with Adobe Photoshop, although a number of other graphics apps can often import them (eg. Affinity Photo) but with the risk of losing certain features. The advantage of Photoshop files is that they can accomodate layers, so several editable graphic elements can be provided in a single file and then manipulated as required.
EPS (Encapsulated Postscript) is an industry-standard vector file format that can be used with most software that accommodates vector artwork.
SVG (Scalable Vector Graphic) can be used for print, but is not as versatile or universal as EPS. It was created more as a vector format for the web and is not designed to handle large amounts of detail on a big scale.
AI (Adobe Illustrator) is a file format specifically for use with Adobe Illustrator, although some other design apps can often import them. In turn Illustrator can export vector images to other file formats.
PDF (Portable Document Format) is a good universal file format for print as it can contain both vector and raster images together. It can not be easily edited, unless you have the right software (eg. Adobe Acrobat Professional) although there are an increasing number of online editors.
If you are just using one of the Logos For Shows templates to add text to, then you'll just need a basic flat image file - JPG would usually be perfectly adequate.
If you want to make up your own layout then the best option would be PSD (Photoshop) where you can manipulate the layered file. If you don't have access to Photoshop then the different graphic elements can be supplied as flat files for you to use - perhaps a mixture of JPG, with PNG for images that require transparency, or PDF could do the same job.
If I'm supplying a full poster, with art and text all set and ready for print, the best option would be a PDF file, with a mixture of raster images for the art, vector for any logos and graphics, and keeping a font 'live' rather than converted down to a rasterised flat image.