To begin with, there is one thing called 大写 (daxie, “upper case”), in contrast to 小写 (xiaoxie, “lower case”).
小写：一二三四五六七八九十百千 - 元
大写：壹贰叁肆伍陆柒捌玖拾佰仟 - 圆
Daxie numbers are only used in finance in order to protect against falsification, because they contain too many strokes to modify. For example, 一 can be easily modified to 二 or 十, but 壹 cannot be modified. Therefore, daxie numbers are usually seen on invoices, receipts, cheques, promissory notes, etc, in order to protect against falsification.
The tamper-proof technique daxie has been used for over a thousand years since the Tang dynasty, invented by the empress regnant Wu Zetian (武则天), and enforced by the emperor Zhu Yuanzhang (朱元璋). It has been tested for so long time as the best practice of tamper resistance. Therefore, daxie numbers finally became the tradition of finance, and are now printed on cash.
However, when we write it down, we still use xiaoxie, like 一元钱, unless we are really writing financial documents, such as receipts and cheques. Daxie numbers are regarded as the specific jargons that should be strictly limited in financial area.
一块钱 is the colloquial term of 一元钱, because in the past the money was only made of metal.
Colloquial: 块 毛 分
Formal: 元 角 分
壹圆 is only used on invoices and receipts, and printed on cash.