The funds you deposit at the beginning can be used to pay multiple seeders. You have one "ledger channel", funded by that on-chain deposit, which is being used to open a "virtual channel" for each seeder you connect to.

There's a bit more about it in this post: https://blog.statechannels.org/channels-funding-channels/.

The budget concept is a security measure between the app and the wallet, so that the app code only has control over a fixed amount of funds in the wallet.

Within the app context, an unlimited number of channels (up to the budget capacity) can be opened. The video at the top of the blog post is an example of a single user downloading from multiple other leechers & seeders while simultaneously uploading to other leechers.