Avalanche is not connected to Binance Smart Chain (BSC) network, although addresses look the same on both networks. If you do a withdrawal from Binance using the BSC network (as BEP20 tokens), funds will actually not arrive on the Avalanche. Network. Instead, they will be sent to the BSC network address you entered, and private keys for that address will be necessary to move them. (NOTE: AVAX should be sent using the C-chain when sending to Metamask, as MetaMask utilizes the C-chain)
As Binance uses the same addressing scheme as Avalanche, private keys that control the address on one network will work on the other. So, if you tried to send to an address on Avalanche that you control, your private keys for that address will work on BSC too. Using Metamask with the Avalanche account, you need to switch to the BSC network, as described here. After switching you should see the same address as on Avalanche.
You probably won't see your funds yet, as they need to be added as a custom token. The address of AVAX BEP20 tokens on BSC is 0x1ce0c2827e2ef14d5c4f29a091d735a204794041. Use that address to add AVAX as a custom token. Follow the instructions from the "How to add a custom token?" heading. After adding AVAX token, you should see your funds.
To learn how to send AVAX from Binance to an Avalanche wallet, please read the following article.