A core is sold by the size of the pipe stub on its end tank, and that stub is usually quoted as an outside diameter including whatever bead is rolled into it. A charge pipe is often quoted the same way, but the coupler between them is bought by its bore, which has to clear the largest feature on either side.
So the number that matters is not the size on either listing. It is the outside diameter of each stub measured over its bead, compared with the bore of the hose you intend to use. Sizing the core and the pipe from their listings alone is how two correct parts arrive at a joint that will not go together.
A rolled bead is there to stop the coupler sliding off under pressure, and it stands proud of the tube by a real amount. A hose that fits the plain section of a stub can still refuse to pass the bead, and forcing it over stretches the bore where it needs to sit flat afterwards.
Measure both: the plain tube and the crown of the bead. If a coupler only just clears the bead, it will be loose on the plain section behind it, and that looseness is what a clamp has to close. A coupler that passes the bead with a little effort seats properly on the tube.
Silicone takes up small differences in diameter, a small angle of misalignment and some length error. It does not take up a step, because a step means the bore is in contact on one side and away from the metal on the other, and no band can close that evenly around the circumference.
It also will not take up an angle at both ends at once. If a charge cooler core points its outlet slightly off the pipe's approach, the coupler will fit and will load one edge of each bead. That edge is where it will eventually split.
Two outlets of identical diameter can still be wrong for each other because of where the stub points. End tanks are shaped around the space available, so the outlet angle is a design decision, not a standard. Compare the angle of the core outlet with the angle at which the pipe arrives.
Check the sensor boss too. A boss that ends up facing the block, the fan shroud or the bonnet cannot be serviced, and rotating the pipe to fix it usually moves the other end out of alignment. Both ends have to be right at once, which is why this is worth checking before the clamps go on.
Assemble the core stub, the coupler and the pipe off the car, with the clamps loose, and look along the joint. You want the coupler sitting square, with the same amount of metal visible all the way round at both ends, and no wrinkle or bulge on one side.
Then push the assembly sideways by hand. A joint with correct overlap resists and returns. One that rocks has the band sitting partly on a bead and partly past it, and that joint will hold while cold and weep once the bay is hot and the silicone has softened.
If the core outlet is the odd one, the cheap correction is a stepped coupler that matches the stub at one end and the pipe at the other, provided there is room for its length. That keeps the intercooler and the pipe as designed.
If the mismatch is in angle rather than diameter, a stepped coupler will not help. The decision rule is simple: a difference you can measure with a caliper is a coupler problem, and a difference you can only see with a straightedge along the run is a pipe problem. Fix the one that matches the tool that found it.