Your charger is smart enough to be able to handle the (slightly different) charge needs for the two different types of battery, though I don't know if it is adaptable enough to figure out cell-pack voltages and combinations.
Choosing NiCd as an example. The fast-charge type use "sintered plate" or similar tricks to vastly increase the area available to the chemical mechanism. The so-called mass-plate and others may be engineered for long periods between use, or low temterature. They are made to a purpose.
A NiCd is charged using a constant current because the voltage will not substantially rise to self-limit the current like happens with a lead-acid battery. Cheap wall-plug chargers use a single resistor, and a current typically C/20 to C/10 where C is the "capacity" in mA.hr or A.hr. This is a safe enough level that will not cause overheating or unfortunate chemical change. It takes ages, and if used carelessly to keep "topping up" a part discharged battery, will result in the battery aquiring a "memory" of its usage. Parts of the cell never exercised will deteriorate. From here comes the tip to let the cells discharge as much as possible before charging. Modern builds are less prone to this, but it still makes the charger requirement tough.
Modern chargers use smarter control chips, much developed from the heavy use and casual charging of batteries used for small power tools. If you just charge away at a fast rate, and deliver the constant current x time to get to the nominal "capacity", you then need to charge about a third beyond that because the charge efficiency of the battery chemistry is only about 65%. Depending on the previous usage, you may get there sooner than you think! There needs to be *some* way of detecting that the battery is full. In the case of NiCd, the full point is accompanied by a sudden and dramatic rise in temperature, along with the cell voltage (while charging!) starting to reduce. This change of slope is only millivolts, but it is the signal to cut way down to a few mA maintenance current. Electric drill charger packs often include a diode temperature sensor taped onto a cell, to give a second signal to the charger control chip.
Some chargers will automatically discharge the pack before putting in a charge. These are sometimes touted as being "good" for the cells in eliminating the "memory effect" and recovering cell capacity. Probably the real motivation was they allowed a timed charge without trying to detect full charge state, but I could be wrong for some products. I once abusively overcharged a 1800mAh pack so the plastic covering melted, and the whole lot was too hot to hold. It still worked, though it needed a new covering which I made from heatshrink. I have been known to pulse a 12V car battery in series with a headlamp bulb into dead AA cells. The nickel crystals within had grown to short-circuit the cell. A few tries of this, and the crystals burn out, and the cell accepts a charge. The 50mA ignored, I give it several minutes of 2A. A cell in this state is not worth this sort of attention. You can repeatedly charge/discharge to bring the capacity back somewhat, but I never do. I need very high reliability from batteries.
Forgive that this may have rambled on more than appropriate for your Radio Shack product, but I don't know the item, and I have been the distance with NiCads.