Two parents can both say "we want joint custody" and be picturing genuinely different arrangements. This is not usually a sign that one of them is being unreasonable. It is because "joint custody" is not one thing.
Two different questions, one phrase
Custody law generally separates two distinct questions: legal custody, which is about who has the authority to make major decisions for a child (schooling, non-emergency medical care, religious upbringing), and physical custody, which is about where a child actually lives and how time is divided between parents. "Joint" can apply to either, both, or neither in a given arrangement. Joint legal custody with one parent as the primary physical residence is common, and is still frequently described in shorthand as "joint custody" even though physical time is not equal.
Where the mismatch usually shows up
A parent who hears "joint custody" and assumes it means a roughly equal parenting-time schedule may be surprised to learn the other parent meant only joint decision-making authority, with most overnight time remaining with one parent. Conversely, a parent focused on decision-making authority may not realize the other parent is expecting a specific, near-equal weekly schedule. Neither assumption is wrong on its own; they are simply different definitions of the same shorthand.
Why writing it down resolves the ambiguity
A parenting plan or custody order that specifies legal custody and physical custody separately, and that spells out an actual schedule (which days, which holidays, how decisions get made and by whom when parents disagree) removes the ambiguity that the phrase "joint custody" carries on its own. Two parents who both used the word "joint" but never wrote down what they meant by it are not aligned just because they used the same word. Alignment comes from the document both sides can point to later, not from the word itself.
Where this fits into a case
Because the exact terminology, presumptions, and default arrangements differ by state, what "joint custody" defaults to if a court has to decide, as opposed to what parents negotiate directly, is a question a licensed family law attorney in the relevant state can answer for a specific situation.