If I open a Nimiq Ecosystem Application in different browsers will I get different Wallets?

Yes, each time you open Nimiq Applications with a new browser, created wallets (Private/Public keys) will be stored locally in that browser. In the Nimiq Safe, wallets can be imported and exported, thus, can be exported from one into another browser. If using a Ledger Nano S, the keys are stored on the Ledger and the device can directly be used on multiple computers/browsers without the need to export the keys.