Is focus and priority the same thing?

No, Focus and Priority are not the same thing. While they are related, they serve different functions during a showdown.

According to the Riftbound core rules and clarification FAQs:

Focus

• What it is: Focus is a showdown-specific permission that acts as a "home base." It tracks which player is allowed to start a new chain during a Showdown Open State.
• How it works: Only one player can have Focus at a time. If you have Focus, you have the authority to play an Action or Reaction card to begin a new chain when the battlefield is in an Open State.

Priority

• What it is: Priority is the singular, exclusive right to take discretionary actions (playing Reactions) during a Closed State (when a chain already exists).
• How it works: Priority is used to restrict the game to a single bottleneck—only the player with Priority may act at any given moment.

How they interact

• The "Bundle": When a player gains Focus, they automatically gain Priority as well. You cannot have Focus without also having Priority.
• Retaining Focus: If you have Focus and pass your Priority (e.g., to let an opponent react to your spell), you retain Focus. You have simply passed the right to act at that specific moment.
• Passing Focus: If the chain is empty and you pass, you are passing both Focus and Priority to your opponent.
• Rules Reference: According to Rule 313.4, "A player may not make discretionary actions with Focus unless they also possess Priority."

In short: Focus determines who can start a chain, while Priority determines who can act on an existing chain.