is it a martini or a gimlet?

Eliza had never spent Christmas in a dive before, and this one was miles from Broadway. Since her parents cut her off, she’d frequented places of lesser and lesser repute, until repute was all but a memory.
They were in Tom Slade’s studio apartment. The only objects of note were a typewriter, a record player, a small wet bar with well liquors, and a dirty mattress on the floor.
The rumor was that Tom had a weird cock, but he’d get you high if you let him pretend he was the kind of writer who could land you a starring role.
She danced to Velvet Underground like it was saving her life. Sweet Jane.
“Yes, That’s exactly how I want Carol to move!” Carol was the part he promised her.
Eliza kept dancing. She wanted to change her name to Sweet Jane. Sweet Jane would dye strips of her hair blue and read poetry outside a bodega for change.
“You got any dope?”
“That’s not very ‘Carol.’”
“Oh I think it is. I think it’s ‘Carol’ as fuck.”
“Yeah, I’ve got some.”
He pulled out a cigar box. It was a good brand. Eliza’s father used to serve them to company, (not his private reserve, mind you.) But inside there were no cigars. A dope kit took their place, and it was the holiest Christmas sight Eliza had ever seen.
“Be a doll and fix me one, dahling.”
“Can you fix me a martini?” He asked in return. “Is it a martini or a gimlet? The one with vodka. Dirty.” He broke open the baggie and poured some heroin into the spoon.
“That’s a vodka martini. What do they teach you in public school?”
She danced her way to the wet bar. He cooked the shot.
“They taught me to never take heroin,” he grumbled.
“So I guess you just keep some around out of a generous spirit.” She poured the vermouth and vodka into the shaker.
“Something like that…”
After the shake she saw no martini glasses. None. She had to pour it into a tumbler. The faux pas was almost unbearable. She sobbed softly at the poor martini in its ill-fitting casing, forced to take a form below its station.