Purpose? = Cash value intended to provide a fair value to surrendering policyholder. Reserve intended to define the amount(s) company must “reserve” to ensure they’re able to pay future benefits. Of course, that’s all an oversimplification.
Method of Calculation? – Is at a high level, often much the same but with different assumptions (if we’re talking about the traditional seriatim net reserve values per policy and not company level reserves based on cash flow testing and PBR, etc). Interest earning and expense allowance assumptions are generally more conservative for reserves (ie lower). Also you said “whole life” and not “universal life”. The latter has methods that vary from traditional. And as referenced parenthetically above, reserves are often calculated at the company (or line of business) level because the purpose is ensuring the company can pay future benefits.
Assumptions? – Generally (see purposes above as to why – also often somewhat prescribed by regulations) may differ (mortality, interest, expense allowances).