It's really common and no one will think twice about sending them to you. In all honesty, just ask the designer for the fonts. On the other hand, if your the designer then it matters more and OpenType tends to be more flexible, allowing more typesetting and finessing, alternates, ligatures, etc. If your just needing to print something submitted to you then all you need is the font the designer used. Is there some big difference between otf and ttf formats? Does the MacOS Helvetica Neue version come as otf or ttf? Which one is the most used? There are about 5 billion versions of every font made by random people available for free and then there are the originals, crafted by the foundry. You can turn on 'font substitution' but that lends itself to an entirely new set of problems, a major one being having to do typesetting everything from scratch again. For the long term problem, there's no solution really. Any artwork you receive from a designer should be packaged with the fonts they used so for your immediate problem it may be best to let the designer know you need the fonts. I understand completely, it's a constant problem. It's not about being an 'authentic' file or having the original font bought from its founder, it's about avoiding a 'missing fonts' notice.
