Surprise is different in 5e. In the playtest there was a readiness score and sneaking, now both are thrown together into one surprise roll.
This is essentially true. In the final playtest there were two ways a creature could be surprised. The first way
did require each and every member of an opposing group to successfully hide by contesting their stealth checks against either the perception or search checks of the creature in question. If this was successful, it would establish a state of surprise in the individual and would head-off the second means for determining surprise which was for each creature on
both sides to make a wisdom check versus a readiness DC determined by either their travel pace, if they were characters, or their alertness, a largely undefined quality that only applied to monsters. This meant that at the beginning of a combat encounter each individual could potentially be making two wisdom checks, only the first of which would be modified by any perception proficiency, unless there was some reason for them to be using search on that first contest.
The 5e rules have cleaned things up quite a bit, IMO. The readiness DC is gone, but travel pace still plays a significant role in that a fast pace imposes a -5 penalty to passive perception scores, and anything above a slow pace makes using stealth impossible. The passive score has replaced the readiness DC and is now used as the DC for each creature's stealth check who is attempting to hide, making it the DC to cause surprise in the one whose score it is. Now instead of everyone rolling, perhaps twice, we have only those who are attempting to hide, and thus surprise, making a roll. This seems preferable.
The most notable difference, in terms of this discussion, between the playtest and 5e, is the removal of the language about "one group" having surprise because it "is hidden from the other" from the hard conditions for surprise. A similar phrase is included in the PBR, but it only applies to specific situations that are given as possible examples of surprise. Also of note is that this was not the only way that one could be surprised in the playtest, as I have outlined above in terms of failing to hit one's readiness DC if an entire side has failed to hide.
Which means "catching someone in a moment where he is not prepared for combat".
Someone in a fight is always prepared for combat.
... unless that someone is surprised. Surprise is determined before combat begins but it doesn't go into effect until the first round, so those who have been surprised can certainly be said to be in a fight, and yet be in an unprepared state, if that is how you wish to define surprise.