There are design differences, time range differences, and psychoacoustic differences.
Design-wise, yes, they both modulate time delay, although the flanger uses some recirculation of the time-delay signal where the chorus does not. The flanger also uses a shorter average time delay, although there is overlap between the range of flangers and choruses.
One of the principal differences between the two is that choruses tend to produce notches across the entire spectrum all the time, where flangers tend to be designed to leave much of the audible range un-noptched during portions of the sweep, and then "infect" the signal with an increasing number of notches as it sweeps downward. It is this cyclical un-notching and re-notching of the audible signal that creates the most significant difference between the two effects. One of the psychoacoustic consequences of this is that one's attention is drawn to the filtering effects of the flanger (since the notches come and go), but drawn to the pitch modulation effects of the chorus (since the notches, though moving around, are always present). This is, of course, helped along by the amount of pitch modulation that occurs, or is easily produced, by the respective delay ranges. For flangers, unless they sweep to a long-ish delay (i.e., into chorus territory) and have lots of modulation depth possible, the vibrato produced tends to be modest. Once into the chorus delay-time range, significant pitch wobble is easily produced.
To a limited extent, it is possible to transform a chorus into a flanger by simply chopping down the delay-time range. If the default range is, say 3-10msec, and you cut that by half, down to 1.5-5msec (for example, by dropping the clock capacitor from 100pf down to 50pf), you'll get something that starts to sound swirlier and vaguely flanger-like. But it's a far cry from the real deal. First, the chorus won't have recirculation built in, so the flange-ey sounds will have limits to their intensity. Second, the lowpass filtering needed to keep clock noise out of the final output will be set lower the longer the delay times aimed for. So, there will be a portion of the sweep where you may not even get to hear the notches because they are above the cutoff frequency of the filtering. Though, that would depend on the specific make of chorus.
The other aspect is the type of sweep. Because the notches only jiggle around a bit, you can't really notice them moving much in a chorus, so there is little need for slow speeds. Consequently, you'll find that the range of sweep speeds tends to be much wider in a flanger than in a chorus. That can be fixed, but a stock chorus will never really sweep slow enough to produce pleasing flange tones unless it is deliberately designed to cover both types of functions. The other thing is that at slow sweep speeds, whether it is a phaser, or filter, or flanger, the ear tends to prefer nonlinear sweep that gets slower as it reaches the "turnaround" near the bottom of its sweep range and speeds up as it reaches the turnaround at the top end of the sweep range. After a certain point, however, once the speed gets fast enough (and we'll arbitrarily designate "fast enough" as being in the vicinity of 1hz), a simple linear triangle sweep is perfectly fine, and may even be preferable at faster speeds or with greater sweep width settings. So, the modulation circuit for a chorus can be different for a chorus and flanger, not just different in terms of the speeds covered.
In the case of the CE-2 and BF-2. The clock circuits are very similar, with nothing that screams out at me "Different type of sweep" (except that the BF-2 circut can attain slower speeds than the CE-2 circuit). One should, in principle, be able to adapt the variable range function of the BF-2 to the CE-2 sweep/clock circuit.
Note that the Depth control in the preponderance of such LFO+Manual-Sweep circuits is really more of a Source-Blend control. That is it combines two voltage sources, one fixed and one varying, and simply adjusts how much of each is combined to form the final control votlage for the clock. It does so in reciprocal fashion: having more of one necessarily means less of the other. It does this so that the resulting control voltage is always within the range that the clock circuitry anticipates. The down-side, of course, is that you cannot simply keep the same sweep width and shift the whole thing to a shorter delay range (e.g., moving a 2-16msec sweep to 0.5-4msec).
If one had intentions of using a single BBD for an assortment of flange, rotating speaker, chorus, and double-tracking functions, you'd probably want to include:
a) defeatable recirculation
b) adjustable, or at least switchable lowpass filtering
c) sweep range adjustment
d) clock range adjustment via switch in addition to variable offset.