there are different types of crutches
Crutches are a really widespread mobility aid, but people still don't seem to know much about them. So here's a list of the different types and what they're good for.
(All image descriptions in alt text)
(plain text: forearm crutches)
Forearm crutches, also called lofstrand crutches, are commonly used by many disabled people. They come in two types, closed cuff and open cuff (one of each pictured above) - there are differences in level of support, stability, range of motion, and ease of use between the two. Which type depends on individual need; closed cuff crutches are generally more stable because they loop around the arm, but can restrict movement. Open cuff crutches are easier to drop but less restrictive. Some compensate by adding a strap to open cuff crutches.
Special edit: my thanks to @nightmaretour for the much better description of the difference between closed cuff and open cuff forearm crutches in the notes. In summary, closed cuff crutches are harder to drop but less suitable for long term use as weight is distributed vertically through the wrist. Open cuff crutches have a wider distribution of weight as they cradle the back of the forearm, and so distribute weight in a more sustainable way long term.
(plain text: platform crutches)
Not the same as forearm crutches! Platform crutches, also called gutter crutches, are helpful for those who can't bear weight on their wrists and/or can't take the vertical shock of each step through their arms. Platform crutches have a more 'braced' position, meaning the user is more stable and the impact distributed, while needing less grip from the hands; however they are notably heavier than forearm crutches. Many models are angle-adjustable, allowing for a position closer to forearm crutches, but can't actually reach the vertical orientation of a forearm crutch. Platform crutches like the above SmartCrutch and Mobility Designed crutch are particularly well known in the Ehlers-Danlos Syndrome community.
(plain text: underarm crutches)
Also called axillary crutches, underarm crutches are commonly used in recovery from injury or surgery, but many disabled people do use them as a daily mobility aid. While the pressure under the arms can be a concern for some (special edit: thank you to @briarpatch-kids for noting that I need to use less ambiguous language here - this under arm pad is not meant to bear body weight and it can cause nerve damage if people do that), underarm crutches can be much more stable than forearm or platform crutches, and there are models designed for everyday use that are lighter than the classic hospital underarm crutch.
Many models of crutch come with specifications to make them better for long-term use. This can include ergonomic grips and soft-touch grips, padding in the cuff of forearm and platform crutches, lightweight materials and construction for ease of movement, flexible ferrule (foot) for a rolling step, specialised ferrules for ice and sand, spring shock absorption to reduce repetitive strain through the body, and more. A person's crutches may be very specialised, and knowing the different types might help you to understand your own needs or the needs of someone else.
I did a similar post about both manual and power wheelchair types that you can find here.