Definitions:
Grid stopper: a series resistor from signal source to the grid of a tube. The "output" of the resistor must be the grid.
Grid reference resistor: a resistor from grid to ground.
It sounds like you're asking why a voltage divider (coupling cap -> series resistor -> grid reference resistor, with output between series and grid reference resistors) reduces signal level, but a grid stopper and grid reference resistor don't. After all, the latter scenario looks just like a mirror image of the former.
That's because the grid is an open circuit; there's no path for current to go anywhere under normal conditions.
Look up Ohm's Law and Kirchoff's Rule for series circuits. Resistors don't just "divide voltage".
For division to occur, and current must flow through series resistors. The current results in voltage drops across each resistance, in proportion to their resistances. The typical voltage divider has an a.c. voltage across it (from coupling cap to ground), which forces a current through the resistors, which then define a voltage drop across each resistance. If you take your output from the junction of the two resistors, then the output a.c. voltage is smaller than the voltage applied to the input of the voltage divider.
When a coupling cap output is applied to a grid reference resistor to ground, and then on to a series grid stopper, the only path to ground is through the grid reference resistor. The "output" of that resistor is the same as its input, and there is no voltage division. The grid stopper does not divide the voltage which is then passed to the grid, because there's no path from grid to ground, no current, and therefore no voltage drop.
You could take an alternate view, and assume there "must" be some kind of current flowing through the grid stopper and into the grid. If no current flows, the apparent resistance of the grid is infinite. If voltage is divided by the ratios of the resistances, and the grid stopper is much less than infinity (and it is), then all the applied voltage is left across the grid. In other words, no voltage drop.
The basics are very important. Ohm's Law, Kirchoff's Laws, the behavior of series, parallel and series-parallel circuits are key building blocks you can't escape if you really want to know how this stuff works. Once you know these items (and how they work with a.c., capacitors and inductors), then most of the function of tube circuits becomes obvious, or very easy to learn quickly.