Hi! ：）
第一个 yours truthfully 是美国式英语不规范的,一般不用或很少用.其他 postscripts 的基本区别如下：
yours faithfully 是很正式的 British English and is used to unknown person （对陌生人）in business correspondence,the one you address as Dear Sir/Dear Madam
yours truly is used to slight acquaintance,是美国式英语,跟英国人用的 yours faithfully 差不多,you use it to the one you address as Dear Mr/Ms + (his/her) name
yours sincerely 或 sincerely yours 也是标准的 British English and is used to acquaintance,friendly but not intimate
此外还有 With respect,also 很正式.
现在很多人一般用最简单的 Sincerely 或者 Regards 或者 Best regards.
对朋友可以用 Best/kind/warm regards/Love （girls' to each other) 等等..
Have a nice day