An American wheel has 38 pockets: 1 to 36, a zero and a double zero. A European wheel drops the double zero and has 37. Payouts are identical on both, and that is exactly where the difference comes from.
A straight up bet pays 35 to 1. On an American wheel it lands once in 38 spins, so betting 1 on a single number returns 36 on average out of every 38 staked. That gap is the 5.26% house edge. On a European wheel the same bet lands once in 37 spins and the edge is 2.7%.
Over 100 spins at a stake of 10 the expected cost is about 53 on an American wheel against about 27 on a European one. Nothing about the wheel feels different while you play; the difference only shows up over a long session.
The practical takeaway is that the bet type barely matters for the edge — every bet except the five number bet carries the same 5.26% — so choose bets by how much variance you want, not by how good the payout looks.