The least spooky version of the teleporter moves you atom by atom very quickly. There is a point where half of you is on each side of the transmission, but everything stays alive the entire time and you're just fine as long as the process finishes. For optimal results you might also imagine there's a part of the machine that preserves the interactions between the two halves of you so there's no misalignment issues and it doesn't matter if it takes a minute to process your whole body. Same atoms, actively alive the entire time, hard to take issue with that version.
This is distinct from the kind of teleporter that makes a copy and kills the original.
And Star Trek is... Okay looking it up it apparently converts you into an energy being that is still fully alive and conscious and mobile, then sends that. Let's ignore Star Trek.