There are transactions, and blocks. Both have their own unique identifiers, which are calculated as a hash of all the data in it.
When a transaction is included in a block, its hash (txid) doesn't change. It just becomes part of a block. That block also has a hash, which depends on the hash of the parent block, as well as on the hash of all transactions included in it.
So no, not all transactions share the same hash. Their hash is simply the hash of their data, and once created and signed, that hash cannot change without invalidating the signatures. Including it in a block doesn't change that.