Frequency range vs frequency response

I should know this but am still fuzzy on it. Could someone explain the difference between frequency range and frequency response when looking at specs of loudspeakers? I know specs are only part of what you base a purchase decision on but which one of these tells the truer story about how low they can reproduce bass levels? Each loudspeaker has a low end value in HZ for these two measurements but they differ. Which one gives you the best idea of how low it can go? What's the difference? Many thanks.
The best is to see a plot of anechoic frequency response in a reputable lab like Canada NRC. Speaker Measurments

Most of manufacturers cheat on frequency range specifications (use in room boost or use loose definitions of range).
'Frequency range' is simply the range, usually expressed from Hz to KHz, that a given device will produce. It tells you nothing about the amplitude variations within the range. 'Frequency response' is usually specified as having a certain amplitude tolerance, such as "±3db", which means that the device is able to produce sound with the range specified at no more or less than 3db from the reference level at any frequency. A plot is much more useful. See the plot below, top graph:
The short answer to your question is "response".

Range tells you "yes, technically the speaker can play that frequency". Response simply adds "and here's how loud that frequency will be played in relation to a baseline reference".

Response is typically quoted as being within plus or minus 3dB of the baseline - this would be considered roughly "flat" or "good" response. As you get closer to the range extremes, frequencies will be played at lower and lower volumes eventually to the point where it is played so quietly it makes no difference to you.

Bass at -6dB absolutely adds to the music, even -10dB does. If you can get a look at the response curve of a speaker it will give you a very good idea of where "useable", "hearable" bass dies off.
You may have noticed on the link I gave above that some speakers go lower than others. This does not necessarily make them better. You need to look at off axis response, distortion and impedance load in order to get an idea if a speaker will sound good.

Compare Dynaudio Focus 110. To the Dynaudio Confidence C4.
Obviously apples to oranges here as the C4 is TEN times the price of the Focus 110.

You will notice a similar frequency "range" (anechoic) but the similarity ends there.

Focus 110 is a small ported design and it shows up as oodles of distortion and a nasty sharp cliff drop in ultra LF (12 db/octave). Of course, for a small speaker, the Focus 110 has "astonishing" bass and would make a great near field mini-monitor for a small room even without a sub.

So it only when you look at the distortion figures that you realize that the C4 is a far better speaker (as it should be given its price). The C4 has distortion less than 1% for much of the useful audio range at decent 95 db SPL levels at 2 meters (live music levels).

Sadly, the Focus 110 has 1% distortion only between 1.5 Khz and 4 KHz (at the higher SPL test levels) with the rest far exceeding 1% and vastly exceeding even the cheapest electronic amplifiers distortion.

In the C4, only the tweeter looks slightly disappointing at high SPL - with the rest of the measurements looking stellar(it begs a question as to why did they skimp on the tweeter on such a stellar speaker?).

These basic measurements only help spot potential problems and it would be better to have more third party data, such as impulse or transient response measurements (waterfall plots). And, of course, good measurements performance just help to narrow down the speaker selection process because nothing can beat careful auditioning.

Thank you all for your excellent answers, links, and technical explanations. I think I'm getting it now. Response is the one to look at more so than the range. That's what I was leaning towards. I'm in the market to upgrade my B&W standmounts in the next few weeks so all the help I can get is certainly appreciated. Distortion is another important measurement to look at as well. Thanks for that.