I call them, IRL:
"The Original Star Trek", or "The '60s Star Trek", or just "Star Trek"
"Star Trek: The Next Generation", or "Next Gen", or also just "Star Trek"
"Deep Space Nine" or "DS9"
"Voyager"
"The Reboot Star Trek Movies" (can't call them "new" anymore!)
"Picard"
The others haven't come up, so technically I haven't called the rest anything IRL. The only ones that really come up are TOS, TNG, and the Movies. Sometimes DS9 or VOY came up in the '90s and early-'00s, IRL. Not recently. Some people talked to me about Picard when it came out.
Everyone talked to me about the 2009 Movie. It got to the point where I had to come up with a stock answer whenever I was asked, since they knew I was a fan. I'd lie a little and say, "I thought it was great!" The only time Into Darkness came up was one time when someone asked me, "So how much do you hate the new Star Trek movie?"
Though if I did refer to the other Star Trek series IRL, I'd only use the sub-title. When I'm speaking it, I only include "Star Trek" in the name for TOS and TNG.