“theruwan saranai” and "budu saranai" are used exclusively by Sinhalese Buddhist to wish/greet other Sinhalese Buddhist. Its not supposed to be use elsewhere because they are religious greetings. Theruwan – තෙරුවන් - mean the triple gem in Buddhism. i.e : Lord Buddha , his dhamma (Buddhism) and his disciples (Sangha/monks). Budu - බුදු - is a shorter form for Lord Buddha Saranai – සරණයි - means taking/going refuge of something . But in this context it means that may you be protected/helped/supported by xyz. So all in all it means - theruwan saranai - තෙරුවන් සරණයි - May you be protected by triple gem - budu saranai - බුදු සරණයි - May you be protected by the noble power of Lord Buddha Ganbatte kudasai ^_^

"Budu Saranai !" = it mean "May the blessings of the Lord Buddha be with you!". "Teruwan Saranai !" = it mean "May the blessings of the Buddha, Dhamma and Sangha be with you!".