Blockchain is public on the network and can be queried in every offline bitcoin wallet data. The function of bitcoin wallet depends on the confirmation with blockchain, and the effective check is called confirmation. Usually, a transaction needs multiple confirmations to proceed. The lightweight bitcoin wallet uses online confirmation, that is, blockchain data will not be downloaded to the device storage.
Many competing coins of Bitcoin also adopt the same design, but they are slightly different in workload proof and algorithm. For example, the use of equity and cryptography to prove and so on.