What is the name of this cactus?

[Ace]

What is the name of the tall cactus, pickle cactus?

What is this succulent, looks like a cauliflower head?

Thank you for your help!

 

[zigs]

Welcome to the forum

Tall one looks like an Arrojadoa aureispina

Arrojadoa Aureispina Cactus – Kens-Nursery

kens-nursery.com

The small one looks like a Mammillaria "Fred"

 

[XxDetrimentalxX]

I dont think the second one is what you suggested. I would say some species of cholla, or something like it.

 

[zigs]

You could be right, could be one of the Austrocylindropuntias

 

[XxDetrimentalxX]

Could be Austrocylindropuntia Cylindrica:

Other than that, I have no clue.

 

[SeniorCitizen]

#1 Possibly Haworthia.

 

[Marck]

The cactus in the center of the OP's first photo is Cereus forbesii forma monstrosus 'Ming Thing', a monstrose, dwarf form of an arborescent cactus native to Bolivia, Paraguay, and northern Argentina. There has been a taxonomic debate whether the correct name for the species is Cereus forbesii or Cereus hankeanus, so you may find this plant to be listed under either name.
...and yes, there is also a Mammillaria sp. in the first shot.

The cactus in the OP's second photo is an Austrocylindropuntia sp., possibly A. cylindrica. The genus is native to Colombia, Ecuador, Peru, Bolivia, and northwestern Argentina