OTB there's much more psychology involved, cos of body language an' time pressure - to be honest those the things I miss most about it an' probly why I got into the game in the first place 
what makes a move the "best"?
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If you always played a safe move, it would stand to reason that you would be safe. If, instead, your "safe" moves handed over the initiative and your opponent achieved a strong attack as a result, well, they weren't safe moves, were they.
The "best" move can be either an attacking or a defending move, almost by definition. I mean, really, there's no way you can say attacking moves always work or defending moves always work. Though generally I guess in chess it seems it's more frequently better to press for an attack or counterplay than to try and defend a position - but by no means do I intend to imply that it's always better to go on the offense.
In the event that the complete game tree for chess were to be mapped out, it's certainly possible that there might be several "best" moves in a position, i.e. they all lead to a the same percentages of forced wins/draws with perfect play (unless there is a forced loss for the side to move in that position, in which case I guess a "best" move would be one with the greatest percentage of forced-win/draw branches). In fact, given perfect play, it's likely that there are many "best" moves in the sense that all of them have subsequent lines leading to a forced win with perfect play (or draw, if that's the best you can achieve from that position); even if one of them only has a single line leading to a forced win. Anyway I'm going off into semantics here, so eh.
My boxing coach in school used to always say the best punch is the one that has the best chance of knocking the other guy out. Barring that, it's the one where he has the least chance of counter-punching and knocking you out.
It's the same thing in chess, all you have to do is subsitute checkmate for knockout.
Loomis wrote:
If you always played a safe move, it would stand to reason that you would be safe. If, instead, your "safe" moves handed over the initiative and your opponent achieved a strong attack as a result, well, they weren't safe moves, were they.
By "safe" move, I mean "cautious," mainly. "Safe" is actually misleading. I have noticed an instinct to try to "play it safe" in my games, giving rise to cautious moves.
These are all great ideas of what a "best move" should be. But we all try to play what we think are the best moves, and we obviously have varying degrees of success. So we try to improve our best moves however we can. For me, as I explained, I'm trying to change my style. A safe move that loses the initiative is not a good move; and a daring move as part of an attack that fails is not good either.
The "best" move in any given position is the one that creates the greatest possible positive imbalance between you and your opponent. It can either help your position, hurt his, or optimally, both. Obviously, which move is "best" in any given situation is subjective and subject to debate.
Ok, if you mean cautious, say cautious. Here is how I would understand someone who said "I made the safe move". If a position is equal and you have a choice between a move that maintains equality or a move that creates an unclear position and tries for an advantage, maintaining the equality is playing the safe move. Moves that cause your position to get worse are not safe. There isn't always a safe move in a position.
When the topic turns to psychology, playing against players rated much higher or lower, or playing style, lots of people say that the best thing to do is to "play the board, not the player"... play the best move. I agree. But chess paradoxically blends the subjective and the objective... it's about the art of attacking and defending, but many positions have a "best move." Perhaps ALL positions have a "best move," and if human beings could analyze positions properly and deeply enough, we could eventually discern them all. The bottom line is, you can't go wrong by playing the best move in any given position... and if you can keep up playing the best move for the whole game, of course, you wouldn't lose a game (theoretically). But how to determine the "best move"? Many have also said (on this site) that many positions don't have just one "best move," and often several can (seem to) be equally good. I also agree with this.
I have drawn the conclusion that too many "safe," protective, defensive moves led to my handing over the initiative in games (among other problems). So when I play on this site, I take several opportunities to play moves that look interesting, but that I would not necessarily play in a more serious game. I try to counteract my perceived tendency to play too cautiously, but I have fared not much better, because my interesting moves are apparently not very sound. My eventual goal is to get my rating as high as possible. Of course I'm always trying to play the "best" move, but what does that really mean? And which is better: playing safe moves, or playing daring moves?