i get the same plot for both, and unsure about your special function i don't have

i will say: use Module to protect your variables from Global`

for instance, if Graphicsx exists and you assume Globalx doesn't refer to it: you might be wrong. in the case of "x" your safe.

however, if you've loaded packages or been trashing Global`, it may well trick you, tricks everyone at times

use Module[]

Context[]

see what your current context in

f[x_]=x=2; f[x_]=(Unprotect[x];x=2);

make sure your function doesn't try to access in-accessible variables as well, for example if your special function changes x but x is it's parameter, it changes $x???, not Global`x, unless you Unprotect x. i'm unsure how savvy you are about namespace so i mentioned it

?Global`*

see list of all variables in Global` , use ?? to see definitions

Attachments:

Without specifying your function we can only guess... It might compile your function before evaluating, which can lead to trouble. It can do symbolic preprocessing on it, but assumes something, somehow, it could ...... Bottom line: without code, we can't help.

dOfZetaAlt2Opt ?

I mean, we can't really give you much advice without knowing the functions:

Show[
 {
  DiscretePlot[Sin[x], {x, 1, 25}, PlotStyle -> {Red}],
  ListPlot[Table[{x, Sin[x]}, {x, 1, 25}], PlotStyle -> {Blue}, 
   Filling -> Axis]
  }
 ]

just works fine (V11). Always try to minimize your problem; i.e. give us only the 'core' of your code that gives a 'problem'.