Some LDO's specify noise in nV/Hz, others specify it in μV(rms). How do they equate?
The formula from the referenced SE answer is oversimplification. If total noise in a given bandwidth is desired, one must integrate the noise over a bandwidth, and the spectral noise densities at, say, 10 Hz vs 100 kHz are different figures. You cannot just multiply the spectral noise density at 100 kHz by a square root of the bandwidth and have a total rms noise figure for this frequency range. The product gives only valid result for a flat PSD, i.e., for a white noise frequency distribution. Also, when applying the general formulas to DUTs, you should include all the circuit components and usage into your analysis.
You can make an attempt at such research for the designated components: the datasheets you cited contain the graphs of spectral noise density vs. frequency.
The Texas Instruments Application Report AN-104 Noise Specs Confusing? provides a detailed guide on all sorts of terms like signal-to-noise ratio, noise figure, noise factor, noise voltage, noise current, noise power, noise spectral density, noise per root Hertz, etc.
Some documents use a parameter called something like 'accumulated spectral output noise' which is not a measured spectral noise distribution value but rather a calculated parameter that can be used to estimate the rms noise applying the formula 'noise-per-root-Hertz by sqrt-bandwidth product'. Looking into Diodes' datasheet, page 21, the graph 'Output Noise vs. Frequency', I see the output noise value of 0.1 uV/√Hz at 100 kHz. The table AP2210-ADJ Electrical Characteristics, page 19, indicates the output noise e_no of 260 nV/√Hz. Maybe it is an 'accumulated' value, and you can use it to calculate the rms noise at 100 kHz by the simple multiplication formula, but still this value does not include the contribution of higher frequencies and may be inconsistent with the setup for the rms noise measurement.