In the scene when the T-1000 arrived at John’s foster parents' house, he asks for a picture of John (thinking that SkyNet doesn’t have any files of what he looked like as a kid). A few scenes later, the T-800 catches a glimpse of John riding by on his motorcycle and instantly recognizes him as John Conner. How is it that the T-800 has the file of what John looked like as a kid but not the T-1000? Is it possible that John uploaded a picture of himself as a kid to the T-800 when the Resistance captured and reprogrammed him or is this a plot hole?
The T-800 doesn't have a picture of John at that age, as far as we know. But what it does have is a detailed ...
... consisting of John's age and probable location as well as his height (HGHT), weight (WGHT), hair colour & style (HAIR), gender (GEND), eye colour (EYES), distinguishing marks (DIST), facial characteristics (FACI) and build (BILD). When added together these were sufficient to give the Terminator a 99.45036% probability match when it saw him.
On top of that, it also knows precisely what make and model of motorbike John is riding.
a 1990 Honda 125 dirt bike.
The command to listen and watch for this particular vehicle was locked in priority memory under target profile.
By contrast, the T-1000's target profile is painfully thin. It knows what Skynet knows from interrogating John's soldiers; John Connor's name, his mother's name, his approximate age and approximate location and that's about it. On arrival it has to 'fill in the gaps' using external sources like the police computer and a picture it sourced from his foster parents.
It makes perfect sense. The T-800 was sent back in time by John Connor to protect his younger self, just like Kyle Reese was sent back to protect his mother. It stands to reason that, just like Reese was supplied with a picture of Sarah Connor, so he could identify her, the T-800 was shown what young John looked like before being sent back. This is just one point in which the plot of Terminator 2 runs closely in parallel to that of The Terminator.
There is actually a key line of dialogue you guys are missing and is often ofterlooked: when the T-1000 went to Connor's foster home and has asked for a photo of him, John's stepfather casually brings up a "BIG GUY ON A BIKE" looking for John prior to the T-1000 arriving. Basically, the T-800 (Arnold) had already been to visit the house, it just happened off-camera. Odds are he didnt know what Connor looked like either, and also had to see a photo of him first.
There was a guy here this morning asking about him, too.
Yeah, big guy. On a bike. Has that got something to do with it?
The T-800 is an infiltration unit...meaning it can use whatever tactics necessary to get the info it needs to get to its target. He could have given Todd and Janelle a million justifiable reasons why he needed to know what John looked like. Todd and Janelle were already tired of John so when the "Big guy on the bike" shows up looking for him, they probably thought John has done something and gives him up to teach him a lesson.
The T-800 already had his profile stored and came to the house just for the sole purpose of intercepting John before the T-1000 got there but had missed him.