Welcome to the wonderful word of 'synonyms' in English. Here's a thing about synonyms - most of them aren't really synonyms, if you take the simple definition most people will reel out for the word synonym. People will say that two words are synonyms if they mean the same thing. However, the Cambridge definition of synonym is (emphasis added):
"a word or phrase that has the same or nearly the same meaning as another word or phrase in the same language"
So, words that are described as synonyms may have similar meanings with only a difference of nuance, or they might have overlapping meanings that are identical in some contexts, or they might just have closely related meanings that are distinct in detail.
Add to this the wide range of terms we have for laughter, many of which are to some extent onomatopoeic, and there's recipe for confusion. So much so that one man's chortle is another's snicker.
To me, a chortle is a restrained laugh, but not as restrained as a chuckle. A giggle is also a restrained laugh, but is associated with stereotypes of feminine behaviour. Titter and snicker are also restrained laughs, but most consist of percussive or toneless noises related to movement of lips/tongue/throat and without the vocal chords being used.
And another English speaker will understand them slightly differently. Really, mostly we know how to use them based on what they imply other than the actual sound made. A chuckle or chortle is relatively mature and suitable for a grown man. A giggle is supposedly feminine, or associated with small children. A titter or snicker is more expected from an immature person, or when laughing about something that is immature.