Can we determine if a filter is butterworth or chebyshev from its physical topology?
In short, no. The 4 you mention are cornerstones of a myriad of subtley different and unnamed filters that occupy the gaps between those cornerstones. Not just that there are four cornerstones - there are other "named" types too.

See gaussian, legendre and Linkwitz–Riley to see a couple more. There are even two types of Chebyshev filter (type 1 and 2). There's even an inverse chebyshev. There's probably a few more but the subtle ways that one filter can morph into another named type still leaves a lot of gaps.

The named filter types are not just arbitrary - there is some facet of the filter that is embodied in some mathematical ratio or value that is important in distinguishing it from others. Butterworth of course is probably the most obvious - maximally flat pass-band, overall damping ratio of 0.7071 and poles placed at equal angles.