The main difference are the rite of initiation, the time of reception into full communion, and the sacraments given. A good article is from a Catholic Answers tract: How to Become a Catholic. This answer is based on the tract, and describes the process for adults and children who have reached the age of reason (age seven).
The Rite of initiation & instructions
The amount and form of preparation depends on the individual's circumstance. If they have never been baptized they will be asked to undergo the rite of reception into the order of catechumens which begins about a year's worth of catechetical instructions in the RCIA program. At the beginning of Lent, the unbaptized will go through the rite of election. Afterwards, they will participate in three chief rituals known as scrutinies for self-searching and repentance during which they are formally presented with the Apostles' Creed and the Lord's Prayer.
But if the non-Catholic Christians have been baptized, they would not be treated as catechumens. They will still receive instructions depending on the need.
The time of reception
For the unbaptized, the time of reception is usually the Easter Vigil (the evening before Easter Day).
For the baptized, they can be received at a Sunday Eucharist.
Non-Catholic Christians that have been validly baptized (the most important element being the use of the Trinitarian formula), will not receive the sacrament of baptism again, but will be asked to confess mortal sins committed since their baptism in the sacrament of reconciliation. On the day of reception they will receive the sacrament of confirmation and the Eucharist. If the validity of the baptism is in doubt, they will receive conditional baptism.
For the unbaptized they will first receive the sacrament of baptism at which point they formally become Christians, prior to the administration of the sacrament of confirmation and the celebration of the Holy Eucharist.