For the first one, a closer picture of the base of the plant, and seeing how those growths on the right develop, will be helpful. It looks like it has bloomed before. A definite ID may not be possible even when it blooms if it is a hybrid, but it should be possible to determine the general type.
The second plant is not an orchid. It is in the asparagus family, genus Ledebouria (formerly in genus Scilla). Ledebouria socialis is the most commonly grown species but is quite variable so I'm not sure this is that species.
The first one looks like Ionopsis utricularioides,,, based off the plant size, leaf shape, leaf arrangement, and the "ridges" on the surface of the leaf...
It grows as a twig epiphyte, from Florida through carribean, central and south america... Nice small pink flowers.
It likes to dry between waterings, and likes bright light.
The second plant is not an orchid. It is in the asparagus family, genus Ledebouria (formerly in genus Scilla). Ledebouria socialis is the most commonly grown species but is quite variable so I'm not sure this is that species.
It's probably the miniature clone, L. socialis 'Miner.' Yes, I spelled it properly, and that is the cultivar name the Huntington gave it. It is not 'minor.' It doesn't need to be on the mount unless you like watering it a lot. It would do fine in a small container with any fast-draining soil.
__________________ May the bridges I've burned light my way.
Here you see the difficulty of getting an ID for a orchid from an online photo! Six posted replies, all well intended but giving different answers.
A small non- blooming plant is nearly impossible to ID. Better photos of the first plant would help, showing the base of the plant. BTW if it is an Ionopsis, it is planted in a pot that is way too big.