Well I'm getting a lot of humor material, but that's not really what I was going for. Here's the definitions I've always used and the ones used by the other pros I know.
Edge = The odds of a game calculated using combinational mathematics and expressed as a percentage. It is irrespective of play and calculated prior to play. For games such as roulette, craps and baccarat the edge is always in the houses favor (excluding things like malfunctioning wheels and dice manipulation). For progressives, Blackjack, and some non-progressive video poker, the edge can be in the players favor. Of course having the edge is no guarantee of winning as the edge is considered your expectation, results WILL vary, both to the positive and the negative. In this way the edge is like the center of the target, not every dart will hit the bullseye, they simple cluster around it. Depending on the size of the edge the equivalence assurance will vary as well as will the amount of variation. None of that matters to "the edge" as the equations used to calculate edge don't include number of trials in any way, nor do they include variance or standard deviation. Subsequently, your actual results after play do not and cannot influence the calculation of what edge you were playing at, since determining your edge is something one does before one plays. Results simply don't enter into it.
Odds = Often interchangeable with "edge" it is the payback of a bet, or game calculated using combinational mathematics. The primary difference is that the odds of a bet are usually expressed in whole numbers rather than percentages. (I.E. 3 for 2, or 2 to 1). A bet or game's odds are also irrespective of trials.
Short Term = A small number of trials that will not produce statistical significance. There is a precise mathematical formula for calculating this, which takes into account the number of trials and the variance of the game. In video poker the number is very close to 1 million hands. So the colloquial use would literally mean, "less than 1 million hands".
Long Term = The number of trials at a given game where you have a 99% chance of being within 1% + or - of expectancy. For most VP games it is right around 1,000,000 hands. So the colloquial use would literally mean, "more than 1 million hands".
Please note that these definitions are not close to what Rob uses, so if we can't agree on their use, I'm not going to be able to get consensus from Rob. My point with him is that for APs and mathematicians these terms have very specific meanings which are all related to mathematical equations, not layman use and that to converse intelligently we must use the specific not general definitions of the terms.
~FK
References: https://en.wikipedia.org/wiki/Statistical_significance
vpFREE or Wizard of Odds also had a page on the technical use of the term "long-term". I can't find the liink right now but I didn't look to hard.