Well , there is no different between SP and MP actually. I guess you mean the competitive gameplays the devs have advertised before?
When you play in MP and only when all four players select Origin Characters , they will have thier own personal quests , which open to new interactions/outcomes which may end up creating possible conflicts between the four or new problems that you normally wouldnt have.
TL;DR You will get the full experience in SP just fine. The only major different between the two is: there will be a Game Master Mode , which possibly make the main adventure feel entirely different and possibly more challenging depends on the GM or "Dungeon Master"For now , in Act 1 , Origin quests dont create much of competitive moments yet. They all can be avoided , its pretty much all up to how you and your friends want to play the game , either against at each other at some points to add more "spices" into your adventure or choose a peaceful way to solve the personal quests and just enjoy the main story adventure together.
♦ Sebille may kill Lizards that involve in slaving her in the past. She could kill Red , the lizard inside Fort Joy's cave and Stingtail , you could lost a Warfare and Pryo merchants in Fort Joy.
( you could also spare them )
♦ Loshe will try to kill Saheila if talked to , which make her hostile to everybody in the cave. Your friends could stand against her and protect Saheila , after shes dead she can be resurrect but everybody in there will hate her.
Or she can flee , everybody wont be hostile anymore but everybody in the cave will still hate her. Well , if you side with Loshe and killed Saheila , you will be rewards with exps coming from those who u killed , and possibly failed some side-quests tied to them.
...etc
You could also create 4 custom-made origins , that way you can experience thier personal quest and thier exclusive interactions yourself. Keep in mind that they have to be custom-made , Origin characters gained as a companion wont have a personal quest , some of thier interactions with minor NPCs will still remain , NPCs tied to thier personal quest wont.
Meaning...
Sebille wont try to kill Stingtail , Loshe wont be aggresive toward Saheila , Ifan wont be "buddy" with the undead merchant , Red wont get assassinated...etc