Fundamentally the design principles are the same - the concrete doesn't much 'care' if it is cast in its final location or somewhere else then moved when it has cured.
In Eurocode (specifically EN1992-1-1, ‘Eurocode 2: Design of concrete structures- Part 1-1: General rules and rules for buildings’) there is a section ‘Additional rules for precast concrete elements and structures’ which has supplementary rules. That is, the majority of the design is the same, but you get some additional rules to follow.
The additional rules cover transient situations, temporary and permanent bearings and the detailing of connections and joints between members.
The transient rules are mainly because in a precast yard the manufacturer wants to strike elements quickly – well before they reach their final strength, so you’ll be lifting and shifting elements when the concrete is only partly cured. The code doesn’t actually have specific rules to follow, it just says that transient conditions should be “considered specifically” (clause 10.2, referring to 10.1.1)
The connections and joints parts do have some specific rules to tell you how to handles such matters as making a slab by joining individual planks, i.e. how you quantify the behaviour of typical connections between the planks. The codes has rules about treating half-joints, types of bearings, anchorage of reinforcement at support and so on.
Overall, section 10 is nine pages out of 230 in the code, so relatively little and minor additional material.