What native issuance means
The issuer mints and burns on that chain directly and honours redemption against it. The token is backed by the same reserves as on any other chain, and its value does not depend on a bridge remaining solvent.
This is the version with the strongest claim and usually the deepest liquidity once it exists.
What bridged means
A bridge locked the token on another chain and minted a representation here. Its value depends on the lock remaining intact and the bridge remaining able to process redemptions. If confidence in that bridge falls, the bridged token trades below par even though the underlying is fine.
There can be several bridged versions on one chain, each from a different bridge, each with its own pool.
How to tell them apart
By contract address, which is the only reliable method. Ticker variants such as a dot-e suffix are a convention, not a guarantee, and many interfaces normalise them away.
Check the issuer's own documentation for the official address on the chain you are using, and compare it with what your wallet is showing.
Why it affects your trade
Routing between a bridged version and a native one is a swap, not a conversion, and it has price impact. A deep pool for the native token tells you nothing about the depth available for a bridged one.
FBT Swap shows the price impact for your amount, which is where a thin bridged pool becomes visible before you sign rather than after.