Can we say :
At one end it's (something).....and at the other (something else) .
Does it mean the same as "on the one hand ....and on the other" ?
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"on one hand"/"on the other hand" is a common idiomatic expression which (mostly) everybody knows the meaning of, but "at one end"/"at the other end" is not. Just that expression taken out of context does not really have any obvious particular meaning, and I think most people would be confused about what sort of "ends" you're talking about.
This expression can sometimes be used when someone is talking about a measurement scale or a range of options for something (i.e. "at one end of the scale" vs "at the other end of the scale"). If it were being used in this way, however, somebody would also need to specify exactly what scale/range/set they're talking about the ends of. This also rather implies that you're talking about a continuum or at the very least more than two options, and you're only describing the two extremes of the range (with other options falling somewhere in between).
So no, it's really not the same meaning, and it doesn't really mean anything out of context. It might mean something in a particular context, but what it means would depend on what the context is.