Ex-post vs Ex-ante Budget Balance in Auctions Have I understood this correctly?

When I say my auction mechanism is ex-post budget balanced it means that in practice (I have done market simulations) and according to the results my mechanism is budget balanced. whereas, if the mechanism is ex-ante it means we only anticipate that it is budget balanced?

A reviewer of my paper has asked me to explain in the paper what ex-post and ex-ante means. How would you suggest to explain it?
These are widely used technical terms with a precise mathematical meaning:

Ex-ante budget balance means that the expected sum of all transfers is zero.

Ex-post budget balance means that the sum of all transfers is zero with probability one. Some authors require that the sum of transfers is always zero.