No, they do not all have the same features.
But there's very little mention of "upgrading" or any other justification for the changing features: it just happens as the scripts need it to. The screwdriver's various visual changes do not typically have anything to do with changes to its capabilities.
The sonic screwdriver started out as... a screwdriver, nothing more. You held it next to a screw, and it turned the screw while making a funny noise.
Over the years its functionality came and went, but overall the "sonic" bit got more play and the "screwdriver" less and less, until it basically let the Fourth Doctor do whatever the writers needed to get him into the next scene without effort.
This is why the Fifth Doctor's era saw the screwdriver destroyed--the producer felt it was a crutch for lazy writing.
The sonic screwdriver didn't show up again on screen until New Who (unless you count a cameo in The Movie, but it didn't do anything). Now it's a magic wand which can do just about anything, including act as a shield and a ray gun, but frequently it's not used as an actual screwdriver when that would be useful.
(It's worth noting that the brief period in New Who during which it "couldn't do wood" seems to have no precedent, but is one in a long line of attempts to limit the sonic's power, all of which are then blithely ignored as soon as they become inconvenient. See also: deadlock seal)