You can access the radial gradient styles in Photoshop (as well as linear, diamond, angle, reflected) throughout the application. Select the gradient tool is the key to the whole thing or select in a variety of panels such as fill content and overlays, etc.
With the tool selected, You can find them (linear etc) for the tool along the control bar along with the actual colors you will be using and other settings such as opacity etc. You can select one at a time. You can also find them in the fill panel and also layer effects panel as well as via shape layers. They are available via a drop down in the overlay as well as glow as well as stroke.
Linear is applied across or diagonal or any angle across an image. The origin of the linear can be inside or outside of the document. It uses the current color / opacity stops (as with radial etc). You can apply it over and over. You can change the angle of application. You can apply it very short so you click and drag and release in a short distance or you can cover the entire document and beyond and the result of the colors generated will depend on the length.
The radial design creates a circular design (there is no elliptical feature but there is a work around). It uses the origin point as well as the length from the start point (clicking on the document) to the mouse release / end point. If you want a small circular design, click with the mouse and release quickly to create a very short length. If you want a large circular design, drag from the center outwards beyond the bounds of the document.
Sadly, the application has no repeat feature (some applications have this feature such as Clip Studio) but you can create all kind of ring designs by using alternating color stops in the editor, so select radial and then go to the editor by clicking on the current preset in the top bar and then adding alternating stops such as black and white and black and white etc. Space them out at 5% or 10% each time.
There is no elliptical option but you can use the radial and then transform that. Select the tool from the tools panel and then go to the editor by clicking the preset in the control bar and add a 0% opacity stop at the furthest right (if you have a stop there already, shift it slightly so you can add a stop at 100%). You will then have transparency and an edge to your preset which you can now apply to the layer. Once applied, go to the layer menu and smart objects and convert to smart object and then transform the layer via the edit menu and transform to squeeze the design into an elliptical shape (or actually any other shape if you use warp tools as well)
Select the angle and it will generate a conical design and you can set the origin any where and the design will fill the selection or the document. The colors will go from 0 to 360 degrees and if the colors are the same for the first and end stops then you will create a smooth design. If the colors are different then you will see a sharp edge in your art (which can be useful)
This creates a repeat of the existing preset and reflected back. If applied across the entire document say from left to right it appears not to work. Apply it from the center or inside the document and go outwards then you will see the reflection.
It creates by default a diamond design but it can be drawn at 45 degrees and creates a square design. You can position the start point anywhere and can use any length to create a small or big design.
There is a final one (that is not added to the other areas of the application) and this can be found when you select a shape and then go to the layer menu and layer effects and go to the stroke section and select fill type and go for gradient and then go to the drop down you will shape burst at the bottom of the list. The scale has no effect nor does angle (I am surprised they are available) however you can use the size field at the top of the panel.