What is the difference between Shaper DPS and tooltip DPS?
The Shaper has 40% elemental resistances, 25% chaos resistance, and 66% reduced curse effectiveness. These effects can significantly reduce the damage that many builds can deal against him, especially builds which rely on elemental damage and/or curses.
The same properties are present on many other endgame bosses, like The Elder, Shaper guardians, Elder guardians, and Legion generals, as well as in lesser forms on Atziri, Delve bosses, Abyssal liches, Incursion architects, etc. As such, "Shaper DPS" is a useful proxy for a build's effectiveness against endgame content.
Additionally, "tooltip DPS" generally refers to the number displayed on the in-game tooltip. This number is calculated in a relatively simplistic fashion, by summing all types of damage dealt by a skill and multiplying by attack/cast speed; it does not take into account other effects which may boost a player's effective damage, like elemental penetration, debuffs placed on enemies, conditional bonuses, or damage-over-time effects you can cause such as ignite, bleed, or poison. (It is also entirely ineffective at calculating DPS for skills which deal damage indirectly, like minions, traps, or mines, or for skills which are triggered by Cast on Critical Hit or other trigger supports.)
"Shaper DPS" is generally calculated using the third-party Path of Building tool, which can take most of these effects into account.