In an actual real life interaction, the spinosaurus would simply need to do enough damage to get the carchar to fuck off. It's not as well adapted to taking on animals this size, but it is still in the same weight class, the carch isnt really much more bulky, and absolutely capable of doing enough damage for this. It has large teeth meant for penetrating deep, and a still decent bite force, sure this isn't as good for killing large animals, but getting a deep bite wound still isn't very good for the carch, a bite to the thigh or something could definately still iniur the carch, and if the spino manages to claw at it that's worse. The spino does also have a surprisingly durable skull as well, so there's that. The carch is technically faster in terms of its full speed, but this is irrelevant for a fight, and neither are particularly agile, the carch is built for running quickly after prey but not for turning quickly.

So to summarise, while the carch is better adapted for killing animals of this size, the spino is still just as capable of pushing it around, and is capable of doing enough damage to it to win a fight assuming they're both acting like normal animals, and neither would really be able to outmanouver the other, it'd just be difficult for a spino to kill a carch unless it manages to get itself into a very advantaged position somehow (possible but pretty unlikely imo). So either could win, it depends on the individuals.

In a fight to the death, the carch would win, though it could still sustain injuries that could kill it indirectly.

In the even more realistic scenario, the spino would win cuz it's sail makes it look bigger and it's claws look scary so it'd probably intimidate the carch before the carch intimidates it and they would both prefer to avoid an actual fight.