save: To save is to commit changes to a permanent state in a format that the application can natively utilize(keeps the file format). To export is to change the data format so that another application can utilize it. (changes the format for example from png to jpg).
What's the difference between saving as PDF and exporting to PDF?
Save as PDF is easy to understand, save current document as PDF file what will change title and/or extension in document tab in Photoshop, for example, and you will continue working with saved PDF file. Export as PDF means export current file as PDF but keep file as it is in . indd file format, for example.
Is it better to export or save as?
A regular Save As just saves the file as-is, about all you can do is set the jpeg compression level. The Export function gives you several options to reduce file size while giving you a live preview of the result.