This article aims at investigating the extent to which the algorithmic nature (i.e., mining process) of cryptocurrencies might influence their dynamics and interaction with some major economic indicators. Our study observes that proof-of-stake based cryptocurrencies are less correlated with other crypto-assets offering more opportunities for diversifying portfolio strategy. We also observe a positive correlation between the proof-of-work based cryptocurrencies and the oil price. This article discusses these matters and suggests that the differences in cryptocurrencies' dynamics are more related to their service or purpose rather than their mining protocol. This claim contributes to the current debates on the intrinsic value of cryptocurrencies and it is illustrated with a discussion of the Stellar (XLM) and Ether (ETH) cases. Beyond our empirical results, our article suggests that, the liquidity and the returns dynamics of cryptocurrencies might be affected by two different aspects. Precisely, the former appears to be influenced by the economic service for which these cryptocurrencies are used, while cryptocurrencies' returns are more reactive to the way their cryptographic validation is operated. Our findings also suggest that an analysis through the economic service/purpose of cryptocurrencies is actually appropriate to understand their dynamics in relation to economic indicators. This perspective implicitly questions the monetary aspect often associated with cryptocurrencies and it calls for a more categorized research (by economic purpose) of cryptocurrencies whose potential intrinsic value would then be related to their economic purpose.