The two types of apostrophes are called the straight apostrophe (‘) and the curly or smart apostrophe (’).
The straight apostrophe is the one you typically find on a keyboard. It is a simple vertical mark and is often used in programming and plain text. This type of apostrophe is also known as the typewriter apostrophe.
The curly or smart apostrophe is more stylized and is often used in formal writing. It curves to the right and is commonly found in word processors and typeset text. This type of apostrophe is preferred in professional and academic writing because it looks more polished and is easier to read.
Both types of apostrophes serve the same purpose: to indicate possession or to form contractions. However, the curly apostrophe is generally considered more aesthetically pleasing in printed materials.