Aesthetics vs Metaphors
Skeuomorphism in UI is defined as something that uses real life 'metaphors' to help people get familiar with a completely new interface, its that part of the design which is meant to convey confidence to the user, that what he is deleting will go into a sort of digital trash-can, that an app is a digital notepad of sorts where you can write things, its the interface to on which hinges the app's usability. its a part of design more than it is of the aesthetic.
Flat Aesthetic: Its not an interface, its just a method of conveying an interface. There is nothing like Flat UI. It is only Flat Aesthetics that we talk about when we talk of Flat UI. Flat Aesthetics are a way of conveying skeuomorphic or non-skeuomorphic elements.
Glyph Buttons VS Text Buttons
A graphical user interface (GUI) was designed in the early 1980s to help the humans get familiar with a computer. A command line interface couldn't achieve that. Skeuomorphic elements like a trash can were put on the screen to tell people where to put their discarded files, a pencil generally denoted an option to edit, a ticking clock meant you had to wait. The same happens when we design an interface for a touch-screen. We need to convey our message to the user and for that sometimes, the use of metaphors is necessary.
Buttons on a computer screen are so much more different than buttons on a touch screen. A touch screen is usually controlled by our hands (which are less precise in pointing than our hands) while we use point and click devices like a mouse on a computer screen which are more precise. Using a text button on a computer screen can be helpful because pointing at a text button on a website with a mouse becomes much faster than pointing at a glyph button on a website. Things get reversed on a touch-screen, our fingers occupy a larger area, they need larger buttons and for that a glyph button is much better. Its like the Serif vs Sans Serif Debate, Sans Serif is much better on a computer screen while Serif is much better on a printed paper. The same's with Glyph buttons and text buttons.