When asking for the bill at the end of a meal,people usually say 埋单 or 买单. I guess you already know that 埋单 comes from Cantonese. While the connection between Cantonese and the rest of China gets closer day by day,the latter took the Cantonese word 埋单but use the homonymic word 买单. In Cantonese,people use埋单instead of 买单 when paying the bill for a meal.Actually the two words are different in Cantonese. In other parts of China,people say 买单.You can also say 结账.But I think 买单 is more common.(服务员，买单。) 结账 and 结帐 are the same.They are often used in accounting. And 结账 is better in writing Chinese.

In Taiwan, both of them are commonly used! but I usually use 結帳！ 結帳sounds more gentle!

高档酒店里通常讲 买单（埋单），抵挡一些的小餐馆一般讲 结帐（结账）

结账and结帐have no differece. 两者没有区别，是通用的。

I think these two words don"t have too much difference, the word of 埋单or买单，was used in high-class restaurant more I think, and in the situation that you want entertain someone else, I think 埋单or买单 is more implicit and polite