Assertions are made by the figures in the financial statements. For example, if the SOFP show receivables of $350,000, this means that the receivables exist, are valued properly, belong to the client, are complete and so on. You don’t audit a figure: you audit the assertions it is making.
Representations are made by management to the auditors eg stating that the laiblities are complete, that they have no intention of closing down part of the business, that they think all inventory will sell for more than it costs.