The passive construction is correct. Your two example sentences are both correct, and they mean opposite things.
The simplest case is the active voice subject/verb/object sentence pattern:
John cooked the steak.
The action of this sentence is in the verb "cooked". The subject "John" performs the action. The direct object "steak" receives the action.
We can form a sentence that has cooking as its action and has the steak as the thing that receives the action without even mentioning John:
The steak was cooked.
This sentence is passive. The subject doesn't do anything, doesn't cause this action. There is still some action, but that action happens to the subject instead of coming from the subject.
Direct objects aren't the only possibility. There are also indirect objects.
John cooked Sally a steak.
In this sentence, no one cooks Sally. She doesn't receive the action. She also doesn't cause the action, the way that John does. Instead, she receives the benefit of the action. She also receives the steak.
We can form a sentence with Sally as the subject, without changing her role in the meaning of the sentence. That is to say, she can remain the beneficiary or the recipient instead of the actor, even as a subject:
Sally was cooked a steak.
This example looks very much like the structure of your first sentence:
You were given some money.
The action is giving. The thing that receives the action is "some money". The thing that receives the money is "you". This sentence does not tell us who did the giving.
Your other example sentence is in the active voice.
You gave some money.
In this sentence, the subject "you" does perform the action.
There is a difference between grammatical roles (like subject, direct object and indirect object) and semantic roles (like agent, patient and beneficiary). In my sentences with John, Sally and the steak, "John" is always the actor or agent, Sally is always the beneficiary or recipient, the steak is always the patient. However, all three are the subject of at least one sentence above.
The sentences where the agent "John" isn't the subject are passive voice sentences.
In your sentences, "you" is the subject of both. In your active voice sentence, "you" is the actor or agent. In your passive voice sentence, "you" is the recipient.