Distribution amplifiers (DA) are generally capable of handling fairly strong signals. They are also designed for installation in a protected environment though you may find some exceptions. These are appropriate for overcoming loss due to splitting and long cable runs. An underlying design assumption is that the signal arriving at the input of the DA is at least of moderate strength after being carried through some length of coax.
Preamplifiers are generally intended for installation in an exposed location at or near the antenna. Some preamps are designed for use in weak signal areas and may overload if used where there are one or more strong signals present. Preamplifiers can be designed to handle a mix of strong and weak signals. You need to choose the correct design based on your application.
Preamplifiers are intended for installation near the antenna. This is so that weak signals will not be degraded further by a long run of coax. Once a weak signal has been weakened to the point of being buried in noise, it can't be recovered by amplification which amplifies the interfering noise as well. When you have weak signals to deal with, whether mixed with some strong ones or not, a preamplifier at the antenna is a better choice because the signal would be lower in quality after traveling through coax to a remote amplifier.
After reviewing your TV Fool report again, I still suggest you use a preamplifier mounted at the antenna. Unless you have a lot of splitting to do and/or some unusually long runs of coax, a DA is not indicated.
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