You can create and save a Tool Preset for any tool, which will remember settings that you choose for that tool, so you can quickly and easily select different presets and settings for a particular tool. The degree of usefulness of presets varies, depending on the tool.

You can reset any tool back to its default settings by right clicking on the Tool Presets button and select Reset Tool. Take care not to Reset All Tools, unless that is intended.

There are three options;

Shape Create a shape layer and color it.

Path Create path, which you can then easily convert into a selection.

Pixels You can apply the Rectangle tool directly to the pixels in the selected layer, but this will make changes directly to those pixels, which is destructive editing. Alternatively select the Path option in the Tool Mode, which you can turn into a selection, and then apply it to a Layer Mask. This option is non-destructive and permanently editable.

Choose from different Fill styles: Solid Color, Gradient, Pattern.

You can also select from recently used colors, or from a range of colors, arranged in various groups.

A Stroke in Photoshop is an outline. Strokes can vary in width, color and style.

You can adjust Stroke Width either with the dropdown size box and the slider, or directly, using the Scrubby Slider (highlighted in red).

Move the cursor over the word "Stroke" and watch for the cursor to change to a hand+arrows. Click and drag to the left to decrease, or to the right to increase the width of the stroke. While dragging, you get a live preview, which is very useful.

The Stroke options are highlighted in green. Click to open the panel shown below.

Choose from different Stroke styles: Solid Color, Gradient, Pattern.

You can also select from recently used colors, or from a range of colors, arranged in various groups.

Note that Fill and Stroke panels are identical, but when the panel is opened from Stroke, options will change the Stroke settings.

The Width of the stroke, also sometimes called Weight.

Choose the line style of the stroke and also choose options for Align, Caps and Corners.

Align: Align the Stroke Inside or Outside the path, or Centered on the path.

Caps: Caps are the beginning and end of a line. Choose from Butt, Square or Rounded Caps.

Corners: Where you have corners in a path, choose from Round, Bevel or Miter.

More Options: You can also select the above 3 options in More Options. You can also customize a Dashed Stroke.

This shows width and height and you can adjust them here, if you need a specific size. Otherwise, it's probably best to asjust them by clicking and dragging handles.

You can combine shapes by adding, subtracting, or intersecting.

Shapes interact in the same way as selections interact. For examples of how selections interact, see Selections Interactions.

Select options regarding Alignment and Distribution.

For more information, see Align & Distribute.

When you have multiple elements, you can arrange them by bringing forward, so they are in front of other elements, or sending back, so they are behind other elements.

Bring Shape to Front brings the shape to the front, so it is visible over all other shapes.
Bring Shape Forward brings a shape forwards, so it is in front of the next shape. It may still be behind other shapes.
Send Shape Backward Sends a shape backwards so it is behind other shapes. It may still be in front of other shapes.
Send Shape to Back Sends a shape to the back, so it is behind all other shapes.

Set your preference for the path color and thickness for the visible path, while your work. This does not affect properties of the path such as stroke or fill.

Set the thickness.

The default shape option is unconstrained, but you can also select Square, Fixed Size, or Proportional. You can also set the option to create the shape by drawing from the center.

Set the Radius of rounded corners.

This is a "Scrubby Slider". Move the cursor over the curve, watch for the hand and arrows cursor then click and drag left to reduce the radius, or drag right to increase the radius. This will control the corner radius for the next rectangle you create. It won't change the corner radius of an existing rectangle.

Align vector shapes to the pixel grid.

The Rectangle Tool is used for creating rectangle shapes or paths.

As well as creating a regular rectangle, you can add rounded corners, add a stroke and fill, create a square shape, and more.

Select the Rectangle Tool on the Toolbar. It shares the button with the Rectangle Tool, so the visible tool will be the last one used.

It is not necessary to select options before creating a shape, as you can change them later. But I have set the following options to clearly illustrate the steps.
I've selected Shape as the Tool Mode and selected a yellow fill and a red stroke of 46 px.

I have also set the Radius to 0, so I will get square corners.

I have clicked and dragged, to create a rectangle.

While dragging, the preview only shows the path. When you release the mouse button, the fill and stroke will update, as in the next step.

This is the result from the previous step.

Because the Rectangle Tool is still selected and the layer is still selected, we can see the handles and bounding box. These will enable us to resize the rectangle and change the radius of the corners.

I am clicking on one of the corner handles to change the radius of the corner.

I have clicked and dragged inwards, which increases the radius of the corners. Because all the corner radii are linked, when I adjust one corner, it adjusts all corners.

See the next step for the result.

This is the result of the previous step.

All the corners have been adjusted the same.

This is the shape without the bounding box and handles. I clicked on the background layer, so the shape layer was not selected.

Click back on the shape layer to make further edits.

To resize the rectangle, click and drag the corner handle, indicated by the small square blue box.

As you drag, you will see the path changing, but it won't update with the fill and stroke until you release the mouse button.

Click and drag on a corner handle to change the radius of the corners.

To change the radius of just one corner, press and hold the Alt key, then click and drag on a corner handle.

This will be the only corner affected (if you press and hold the Alt key, while dragging).

While you are dragging, you will see the path changing, but the shape won't be updated until you release the mouse button.

See the next step for the result.

This is the result of the previous step, when the mouse button is released.

Only the top right corner has been changed. As I dragged outwards it has reduced the corner radius.

I dragged to the limit, thus changing the corner radius back to 0 degrees, i.e. square.

You can also control and edit the radius of each corner via the Properties panel.

If you can't see the Properties panel, from the menu: Window > Properties.

It may be that the Properties panel doesn't show all the properties.

See the next two steps.

Move the cursor over one of the edges. In this screenshot, I've moved the cursor over the bottom edge. Look for the cursor changing into a double headed arrow, to indicate resizing.

Click and drag to expand the Properties panel.

The four corner properties are highlighted in red.

The chain icon (to their left) indicates that all corners will be adjusted the same.

Click on the chain icon to enable adjusting each corner individually.

Select the desired corner and enter the desired amount of radius.

Here is the result of only changing the top right corner radius.