Terminator: The Sarah Connor Chronicles continuity
In the Terminator: The Sarah Connor Chronicles (2008-2009) continuity, it appears that terminators can't automatically identify one another as terminators via electromagnetic emissions or whatnot.
In S01E01, "Pilot," there's a scene where two terminators -- Cromartie, a T-888 sent by Skynet to kill John Connor, and Cameron, a T-900 sent by the older John to protect his younger self -- were in the same high school classroom, along with John, and neither seemed aware that the other was a terminator until they started blatantly acting like terminators.
Later in the same episode, Cameron was briefly able to fool Cromartie into thinking she was John by wearing his clothes (including a hoodie, with the hood up) and mimicking his voice.
In S02E06, "The Tower Is Tall But the Fall Is Short," Cameron and Rosie -- a female terminator sent by Skynet -- apparently failed to identify one another as terminators initially, despite entering a building at the same time and standing in an elevator together. They did ultimately realise they were both terminators when they attempted to enter the same room within the building at the same time.
In S02E22, "Born to Run," a T-888 -- dubbed the 'Water Delivery Guy' by the Terminator Wiki -- was sent by Skynet to kill Catherine Weaver, but when he confronted her, he appeared to think she was human, seemingly unaware that the real Weaver had been replaced by a T-1001 imposter six years earlier.
In S02E11, "Self Made Man," Cameron recognised Myron Stark -- a T-888 she saw in an old photograph -- because she already had a picture of him stored within her internal database.
In S02E14, "The Good Wound," John Henry revealed to Catherine Weaver that he knew she wasn't human. She asked how he could tell and he explained that when he looked into her eyes, there was "nothing there," implying that her lack of emotion was enough for him to tell she wasn't human.
JOHN HENRY: You're not human.
CATHERNINE WEAVER: Excuse me?
JOHN HENRY: You're not human. You're made of metal. Not the same metal as I am, but metal.
CATHERNINE WEAVER: How can you tell?
JOHN HENRY: I looked into your eyes. There's nothing there.
Terminator: The Sarah Connor Chronicles - S02E14 - "The Good Wound"
Terminator Genisys continuity
In the Terminator Genisys (2015) continuity, it appears that terminators can automatically identify one another as terminators, not via electromagnetic emissions, but through a visual analysis.
Pops opened fire on the John Connor terminator on sight, with a subsequent POV shot indicating that Pops could see that John was made of Machine-Phase Matter.
Pops could also see when there was a piece of a T-1000's mimetic polyalloy mimicking part of a van he was driving.
And the T-800 sent to 1984 to kill Sarah recognised Pops as another T-800 on sight. In this specific instance, the two terminators were the exact same series (800) and model (101), and Pops spoke to the T-800 first, which may have helped to give him away. Then again, it may not have mattered, as these terminators appear to have superior visual capabilities to the ones in Terminator: The Sarah Connor Chronicles.
Other Terminator continuities
I've yet to pinpoint any clear evidence confirming whether or not terminators can automatically identify one another as terminators in continuities other than the two named above.
I checked the scene where the T-800 and T-1000 encountered one another for the first time in the official novelisation of Terminator 2: Judgment Day (1991), but that didn't reveal anything useful, as the scene was described from John Connor's perspective, rather than that of either terminator.
The scene where the T-800 and the T-1000 spoke to one another on the phone suggests they couldn't tell they were speaking to another terminator by the sound of their voice, though. Otherwise, the T-1000 would've immediately known when he was speaking to the T-800 rather than John, and the T-800 wouldn't have needed to trick the T-1000 into revealing that he didn't know the name of John's dog, Max, in order to determine that he wasn't really speaking to John's foster mother.
In Terminator Salvation (2009), Marcus Wright was recognised on sight by an automated defense system guarding the perimeter of Skynet Central, but Marcus was an unwitting agent of Skynet who was intended to lure John Connor to Skynet Central, so it's only natural that the defense system would recognise him and grant him entry; it specifically knew his name, which helps to corroborate that. Not to mention that his metal endoskeleton was exposed through holes in his damaged flesh at the time, so he didn't exactly look like a regular human.