Are a blunder and mistake different things or just two words for what is the same thing?

I am still unclear whether "blunder" and "mistake" are two words for the same thing or whether a "blunder" is fundamentally different from a "mistake."

If these two things are different somehow can someone explain that difference concretely"

It's mathematics, the difference between your move and the top engine move.

I'm not sure about chess.com, but on the open source chess site:

0.5 to 0.99 = inaccuracy

1 to 2 = mistake

>2 = blunder

The exact values are arbitrary, and they reflect the magnitude of the error.

Blunder = big mistake
inaccuracy = small mistake

A blunder is usually when you do a nove that lets your opponent capture one of your pieces for free

A blunder terribly worsens your position to the point that it's very very very difficult to regain the initial balance unless your opponent plays even worse. Mistakes are slightly less terrible than blunders.

Neither a blunder or a mistake may worsen your position. Examples: a mistake may be missing a free opponent piece capture and a blunder could be missing  a free mate in one.

Even that's technically worsening your position. Your position is now worse compared to your position had you taken those free hanging pieces.

inaccuracy = slightly bad

mistake = bad

blunder = really bad

missed win = very very bad

If you are referring to how this site's postgame analysis judges things, I believe it concerns the numerical value of your error. A large change in the positional evaluation will be a blunder, while a mistake is a small one. An inaccuracy does not alter who has the advantage, but changes it ever so slightly.

When I am annotating games, I consider any move that turns a win into a draw or loss as a blunder. A move that turns a draw into a loss is also a blunder. What constitutes a winning position may vary due to the skills of the players, of course. Generally, something that loses a whole piece (knight or bishop or more) without clear compensation would be a blunder. Positional considerations matter, also.

Sometimes engine will say that giving back some material is a blunder (and it goes from +7 to +4) but in a practical sense that simplification could mean that the other side has no more chance for some counterplay. I would never consider that a blunder.

Yes @NikkiLikeChikki, computer evaluations can be misleading.

Here's a fragment of a game I played this morning. The computer said we each made one blunder. My opponent tossed away a whole piece early, and I did not take it. There was a checkmate threat combined with a hanging rook. In the ending, however, we both made additional blunders. See the notes to the game, which combine mine with the computer's. Hopefully you can tell the difference.

A blunder is still a blunder, even if neither side saw it or took advantage of it. One can argue the semantics of what level of evaluation change constitutes a blunder or mistake. That said, a move that changes the evaluation enough that it would be considered a blunder but that you still can't see how it's a blunder many moves later, is likely still a blunder but probably not a useful metric

Agreed. A "mistake" and a "blunder" are two different terms, but in informal chess conversation, there is little difference and it is somewhat opinionated (since human players usually don't evaluate positions by the centipawn unless they are consulting an engine).

In practical conversation, they are about the same thing - perhaps "blunder" is somewhat worse though. In a formal definition (like an engine using its objective assessment of the position), there is a degree of difference that indicates move strength based on centipawn evaluations. 

Is it? When I do analysis and based on the evaluation, I'll sometimes still mark a move as a blunder if the evaluation warrants it, even if I don't see the why, though I'll still make an annotation of that case. I don't have to understand why a move is a blunder if it is one; a stronger player may be able to look at the position and could explain why it is, even though i can't.

I understand your point and the understanding of the why can make it a moot point depending on the level of the players, but evaluation should be as objective as possible; i.e. the truth is the truth no matter what someone believes

I like Mi-steak cooked medium, and I always use a blender to make roasted butternut squash soup.