The display of an LCD-based monitor will always be pixelated, and the dimensions of the smallest controllable unit (or a pixel, any of the three colours) are precisely defined and unvaried. The screen resolutions that do not match the native resolution of the monitor are averaged into that resolution by the monitor hardware, or are not shown at all. The result on the non-native modes is dependant on the quality of the monitor and the capabilities of internal controller and its software.
The analog old-fashioned CRT, on the other hand, has no "steps" and it will be able to "glide" over a wide range of resolutions, but here it's the grid mask of the CRT that defines the maximum attainable resolution, and the performance of the relatively high-power high-frequency drive circuitry for the three CRT cathodes. (This is not to be confused with the scan/field rates or frequencies, which are independent.) Building a high-definition CRT monitor is/was a costly affair, and the set actually needs to be constantly readjusted as the CRT ages. The plus side of the CRT is that the colours can be "deeper" than in an LCD and thus a better choice for publishing work.
There's no one standard resolution for either one of the types, I'm afraid.