similar in that they both have a vertical shaft that spins. However, this topic has been cover at least 10 times here.
No you didn't screw up. Here's why. A router spins smaller cutters at very fast speed, 8,000 RPMs to 22,000 RPMs, because that's the way they work best. A shaper will spin quite large cutters at only 2 speeds 7000 RPMs or 10,000 RPMs.
The router has a collet for the cutters, a shaper has a shaft and then you can use cutters with a hole through the center, called the bore and a nut on top to secure them.
Shaper cutters are more expensive as stated. Router cutters can come up from the bottom of a panel and make stopped dados or grooves, not so with a shaper unless you are on the edge of the
Shapers are more for large cutters in a production setting like making 1 3/4 to 2 /38" thick rail and stile entry doors, not 3/4" cabinet doors. Routers are noisy even when not cutting, shapers are quiet, smooth and more powerful and yes, more dangerous.
For a woodworker who is not doing production work a router table is just fine. RELAX.