Moodle provides a range of different question types for quizzes which you can see as below when you Add question (from the Question Bank  or within a quiz).
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The most common types are covered below.

Multiple Choice Questions (MCQs)
This is one of the most common question types. You can create single-answer and multiple-answer questions.

Single-answer MCQ
Radio buttons indicate that the example below is a single-answer MCQ.
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See Add a Quiz for details of how to create a single-answer multiple choice question.

Multiple-answer MCQ
Square buttons in the example below indicate that this is a multiple-answer MCQ.
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The process for adding a multiple-answer MCQ is the same as for adding a single-answer question (see Add a Quiz) except that you need to choose Multiple answers allowed.
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You also need to ensure you distribute the scoring proportionately across the correct answer options so the total adds up to 100%.

True/False Question
In this question type there is only a choice of True or False. It is effectively the same as an MCQ but with only 2 responses.
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To create a True False question, see True/False question type on Moodle Docs

Short Answer question
In a short answer question, the student types in a word or phrase in response to a question or to complete a statement (as below). The answer must match pre-defined answers exactly. It is a good idea to keep the required answer as short as possible to avoid missing a correct answer that is phrased or spelt differently. You can specify whether the answer is case sensitive and also use wild cards where spelling may vary.

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To create a Short Answer question, see Short-Answer question type on Moodle Docs

Numerical question
From the student perspective, a numerical question is just like a short-answer question except that answers must be numerical and can have an accepted error range e.g. if the answer to the question below is 3.15, an accepted error of 0.05 will mean that any value between 3.1 and 3.2 will be accepted as correct.
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You can also grade the unit independently of the number to allow for alternative correct answers using different units e.g. 150 cm and 1.5 m. The unit can appear on the left as well as the right of the number e.g. £100.

To create a Numerical question, see Numerical question type on Moodle Docs

Calculated Simple Question
Calculated questions offer a way to create a series of numerical questions using wildcards that are substituted with random values when the quiz is taken. To set up the question below,
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you would specify:

What is the surface of a rectangle in m2 with a base of {b} m and a height of {h} m?

Each time a student takes the question, a different set of values will appear for {b} and {h}. There are also settings to control the range of values and the number of variations.

To create a Simple Calculated question, see Simple calculated question type on Moodle Docs

See also Calculated question type on Moodle Docs for details of the more complex options available with the Calculated question type.

Essay Question
These are used for questions where longer answers are needed. Unlike other question types, they have to be manually graded. A student can type their answer into a text box and/or include an attachment. You can provide a template for them to structure their response.
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To create an essay question, see Essay question type on Moodle Docs

Matching Question
This type of question requires the student to pair two columns of information e.g. cities to countries in the example below.
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To create a matching question, see Matching question type on Moodle Docs

Other question types
For information on all Moodle question types, see Question types on Moodle Docs

Use of images et al in questions
The majority of question types allow for the inclusion of images, sound or other media as well as text in the question stem.
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The same applies to feedback.
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