PSD
PSD is Photoshop's native file format, which keeps all your layers, masks, smart objects and text. It's your working file: as long as you save it as PSD, you can adjust any edit later. For sharing you then export a JPEG or TIFF.
Always save your Photoshop work as PSD so your layer structure stays intact and you can keep working non-destructively. For very large files (over 2 GB) you use PSB, the big version of PSD. Lightroom can read PSD files and show them in your catalog, handy for a mixed workflow. Think of the PSD as your master file and the JPEG as the finished copy you share.
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The presets on this site set these adjustments up for you as a starting point, which you then fine-tune to taste.