There may have been some negotiations with your client about the rates while creating the quote for a job. Those rates that were manually modified in the quote will only be reflected in the Active Quote, once it gets approved. But if your invoice will be based on the Actuals (i.e. what really happened) instead of the Quote/Budget, then those rates need to be copied into the Project’s Rate Card.
To enable this option, go to the fourth icon at the top left of the Budget window and under "Add Budget Rates To Project Rate Card", select either "Ask" or "Always".
When this setting is changed from the Budget window, there is a dialog reminding the User that the change only applies to that specific Project. New Projects will still have it set to the default option, according to the initial configuration in the Server Setup > Financial tab > Add Budget Rates To Project Rate Card (Default).
If this option was set to "Ask", when clicking OK to leave the Budget window, you get prompted if you want to "Add Budget Rates To Rate Card?". This dialog only shows if there is an Active Budget.
See here the resulting Rate Card.
Once you start scheduling these prices will apply over the default from the price list.
If you create this Rate Card after having added some bookings to the Project, then click on "Force Apply" button first. A dialog will ask "Do You Want To Reset All Object Prices To Their Original Prices?". Select "No" to not touch those items which prices you had manually modified. Select "Yes" for the system to refresh the prices on all items with the default price from the price list - this means that discounts or manual prices to any items in this Project will be removed.
If there is an item added several times to the Budget with different prices, the following window will inform that "Some Lines Would Give Ambiguous Rates And Will Not Be Added". In this case, you will need to make sure that the Actuals that correspond to each of these quoted lines will get the correct price because they will not exist in your Rate Card.
Read more about Rate Cars here.