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Prudence is an account concept where you err on the side of caution. Thus expenses are recognized as soon as they are incurred and here is a liability, where as revenue is only recognized when it is realized. Eg If you have an investment in a company that declares dividends of Rs each and if this there they have declared it but it has not been approved by the shareholders, you will not consider this as an income as the shareholders have not approved it. You err on the side of caution. Prudence goes hand in hand with another concept called matching and results in companies have prepaid or accrued income and expenses at the yea end.
Separate entity on the other hand is where in a sole trader business, even though the business belongs to the sole trader, we treat him separate from the business. If the sole trade makes payment for his personal income or expenditure, it is treated as drawings while if he pays from the same bank account the expenses relating to the business, it is treated as a expenditure. Even though legally the sole trader and his business are one and the same, for accounting purposes we treat the separate and hence the separate entity concept.
I have known it as separate entity concept so not exactly sure if you are referring to the same by separate legal entity concept. In a company shareholders are automatically legally separate from the company.