What's the difference between Persona 5 and Persona 5 Royal?

Solution 1:

Persona 5 Royal is similar to Persona 3 FES and Persona 4 The Golden: it's an enhanced version of the base game but with a sequel included (except for Persona 4 The Golden, which doesn't add a sequel).

The most important changes at a glance:

• A sequel in the form of a third semester. The third semester can only be accessed if you managed to meet the requirements before November 17.
• A new playable character and confidant: Yoshizawa Kasumi of the Faith Arcana.
• A new confidant: Takuto Maruki of the Councilor Arcana.
• A new supporting character: Jose.
• The story has been slightly tweaked to accommodate for the additional characters and the new third semester.

Additional changes include:

• 4K 30 FPS support on the PS4 Pro.
• The "Thieves Den" as the protagonist's palace. It is a recreational area unrelated to the story.
• New songs.
• Slightly different Playstation Trophies.
• New costumes.
• New dialogue portraits.
• Lip sync during voiced dialogue scenes (Japanese voiceover only).
• Some unvoiced scenes are now fully voiced.
• Additional scenes (from Persona 5 The Animation).
• Some characters have new voice actors.
• A scene (where one character is being harassed by two men) has had its dialogue slightly modified for the English localization.
• The international release now has Japanese audio included (was a DLC before).
• The international release now has French, Italian, German, and Spanish subtitles.
• A new font to support the additional languages. Some names have been updated as a result, e.g. "Arsène" and "Café Leblanc".

School Life

• A new location in Tokyo that can be visited: Kichijoji.
• A couple new hangouts: An aquarium in Shinagawa, and the Nakano shopping district.
• New activities, such as darts, billiard, or drinking.
• The protagonist can increase his max SP by visiting a temple.
• A clothing shop has been added, where the protagonist can buy new outfits.
• The Justice Arcana is no longer automatic.
• Existing confidant abilities have been modified, and can grant new perks.
• The protagonist can hang out with Caroline and Justine to gain Skill Cards.
• The protagonist can now give gifts to his male confidants as well.
• The protagonist's free time has been slightly rearranged.
• It takes longer to improve the Guts and Kindness Social Stats.
• Most of the daily activities have been modified or expanded.
• There's a new "Daily Assist Command" to help the player during day time.
• The Valentine's Day event has been updated with additional content.
• There is now a White Day event.

Phantom Life

• New Personas.
• Some Personas and Shadows have their attributes, move sets, or Arcanas altered.
• Party members have their skill pool slightly tweaked.
• New skills, and the effects of some existing skills have changed.
• New enemies.
• Accessories can grant active skills in addition to passive effects.
• A new palace for the third semester.
• A new area in Mementos.
• New ultimate Personas for the third semester.

• Akechi returns as a playable character

• New Mementos Requests for the third semester.
• The Velvet Room can sometimes enter a Fusion Alarm state, which allows for the fusion of more powerful Personas, but increases the risks of fusion accidents.
• A new Challenge Battle mode, where the player can battle various enemies. The protagonists from Persona 3 and Persona 4 are available as DLC boss fights.
• Merciless difficulty is now included (was a DLC before).
• Difficulties have been tweaked.
• Unison attacks, called: "Showtimes".
• New types of Shadows: Savage Shadows and Disaster Shadows.
• New collectibles, called: "Will Seeds".
• There is a rare chance to stumble upon "Deviations", special areas with different layouts within Mementos.
• A Grappling Hook.
• Futaba has her own Finishing Touch, a special animation that plays after an All-Out Attack defeats all remaining enemies.
• The behavior of all major bosses has been altered or expanded.
• Lavenza can be fought in Mementos during a New Game Plus.
• Baton Pass is unlocked for all party members from the beginning. There is now a Baton Pass Rank instead. When maxed out, the Baton Pass is now more powerful than before.
• The party members' Shadow Negotiation ability (during Hold Ups) now always works, but only under specific circumstances, which differ for each party member.
• Technical attacks (attacking enemies afflicted by a certain status condition with certain elements) can be ranked up by playing billiard and has a chance to down enemies.
• New status-element combos for Technical attacks, as well as the ability to learn combos from books.
• Guns reload after every battle. You are no longer limited to a certain amount of ammo every time you visit a palace.
• When frozen, enemies temporarily lose resistance to Physical and Gun skills.
• Some status ailments now end upon getting hit. Additionally, Confusion ends 1 turn earlier than other status ailments.
• The Reaper is now immune to the Despair ailment, and is therefore no longer vulnerable during Flu Season.
• The Security Meter in palaces now starts at 40% instead of 0%.
• Treasure Demons can now appear among random Shadow guards.