Yes, it's the same word.
The respective texts in greek are: «τίς μου ἥψατο;» and «μή μου ἅπτου».
The former is simply the past tense of the latter.
Strongs 680 which you reference in the related question, shows examples of both tenses: http://biblehub.com/greek/680.htm
EDIT from comments as requested: The question implies that this verb can have two meanings: one of "to touch" and one of "cling to / to hold on to". This is in reference to the linked question here, which attempts to distinguish "which of the two meanings" is to be understood in that particular biblical passage.
I dispute the meaning of "cling to / hold on to", and note that when people say that it has been cited to have that meaning in some translations, when read in context it seems to mean "cling" in the sense that two hinges 'cling' (i.e. come into touch) and thus "hold on to" each other and fasten together. As opposed to the modern interpretation of "clinging", e.g. of a person to another person, or "holding on to" in the sense of not letting go of from one's grasp or possesion.
Instead, I would argue the two passages are not in fact different in verb meaning, only in context. As we've said in the other thread, I don't interpret the latter passage like that. As a simple Greek person reading it in Greek, I simply read
"mi mou aptou" as
"do not touch" (or more literally translated as "do not touch of me"); in context, one may perceive that to have meant:
"Don't be so shocked. Don't touch me so inquisitively as if I'm a ghost. It's true. I'm still here.".
But yes, it's true that, outside of that context, the phrase
"mi mou aptou" could equally have been used by one to mean
"Don't touch me. I don't like to be touched".
So, while one can make reasonable assumptions behind the true meaning of that utterance based on the context of a shocked Mary and a reassuring Jesus, in actual fact it is so tersely written that we cannot really know for sure what John meant to convey by that account.
So we can only go by what is written, which is "Do not touch (of) me". It is what it is.