Powergaming: Building/playing a character with the goal of overshadowing the other characters in the party.
Optimizing: Building/playing a character that works effectively within a team to meet team challenges..
I disagree with both of your definitions.
(Note: what follows is essentially from another post of mine in a different thread)
There are a few definitions (of powergaming) that have been around for a very long time. Three examples of definitions include
a) an emphasis or focus on character power as defined in the game. This can be as simple as having an attitude that my starting character has to be as good as a special forces/olympic level athlete/whatever, have minimum of x in bonuses, delivering a minimum of x amount of damage, being great at social combat (in a game where social combat is power), etc and viewing the character as "sucks"/"inefficient" if they don't meet this arbitrary thereshold. Also under this character would be focusing upon abilities like domination or social skills in games where those options result in the most powerful characters (hence, dpr is not inherent to to the definition).
b) playing with the goal/emphasis upon accumulating power. In D&D which rewards characters as they level with bonuses, new spells, accumulation of magic items granting bonuses and/or spells, money that can be used to purchase magic which increases bonuses and provides new spells as as characters level in order to level repeat the cycle and grow in power, a player with emphasis on leveling and accumulation of power would be power gamer.
c) Optimizing/ Min-max. For some people, powergaming is Optimizing/Min-Max. However, given a and b above, I don't think a player need be good at min-maxing or even engage in it to be a powergamer. Powergaming is, therefore, an outlook/playstyle.
Optimization is just a tool. It is the prioritizing of available choices/resources to best meet some specific criteria (the concept) rather assigning those resources elsewhere which is why many powergamers and buttkickers engage in it (butt-kickers being those whose playstyle a strong emphasis/preference for combat and butt-kicking being its own playstyle axis). However, optimization, need not be used for power gaming or buttkicking. One can optimize to be best underwater basket weaver, but that is not going to make a character powerful in most games. It just represents how talented the character is. One can also optimize at character creation to be a farmboy psychic warrior who is the best horse racer in his community by assigning resources to those areas as appropriate without maxing out bonuses in those areas or keeping them maxed out over time (see below about degree of optimization being a continuum upon an axis).
Min/Maxing, however, in my opinion and in that of many circles of which I have been part, is viewed as an extreme form or optimization releated to powergaming given that the name is about minimizing weaknesses and maximize strengths (and, as such, about character power).
The other thing that often gets over looked is that power gaming and optimization are not binary. They are each a continuum on separate axis (again, why a&b above do not require one to be skilled at optimization or to optimize at all to be a powergamer). I don't care about dpr, having the biggest numbers or many things about which heavy powergamers care. However, on some style quizzes, I still show some degree of powergaming, because I like having my character to both improve in existing skills and picking up new skills to reflect my character's growth. Improving existing skills and picking up new skills both provide increased bonuses in order to be more effective mechanically and so, under b above, would involve some degree of powergaming which is why I usually get around 25% powergamer on certain tests.
Also, since optimization involves a) prioritization of available choices/resources to best meet a concept with specific criteria (even if either that concept is based upon mechanical bonuses or the character is weak and sucks in strength so assign a low score rather than somewhere else) and b)optimization is on a continuum (meaning one can engage in it to varying degrees), as soon as one starts assigning resources (even if it is ability scores), the player is engaging in some degree of optimization. The only way to avoid it is to generate everything mechanical about the character randomly or otherwise remove generation choice from the player (e.g., pre-made characters, set character templates, etc.) as well as mechanical improvements.
Now, the above does not mean that there are not some people whom power game to overshadow the party, but they are not representative of all power gamers and are a subset whom are jerk players.
The above also does not mean that there are not some people whooptimize to fulfill a role in the party, but they are simply using optimization as tool to meet a specific criteria (i.e., fill a specific role with a specific level of competency). However, filling a team role at a specific level competency is not the only criteria for which someone might optimize.
The real issue with powergamers and optimizers in my opinion is when a player crosses over some arbitrary threshold on either end of the powergaming and/or optimization axis (or should it be axes) and the point conflicts with the preference of the DM and/or other group members. This is more pronounced among those whom are tied to their "builds" and pre-planned builds for multiple levels regardless if the DM tells them it is inappropriate for the campaign. However, this is no different than other playstyle conflicts when expectations clash. For instance, the groups I play with are more about exploration and story "creation" than butt-kicking and powergaming. However we had a method actor type player that was so far over the top and into stealing other people's spotlight that he was just as obnoxious as the powergamer/butt-kicker/optimizer whom would a) complain if we did anything other than combat; and b) told players that they built their character wrong for optimizing for combat or taking the most powerful options. Both got themselves kicked out.
