Are 打算 (dǎ suàn) and 计划 (jì huà) both synonyms for "plan," or are there some additional nuances here?
打算 means 'intend to'(v) ; 'intention'(n) .
'打算' can mean 'to plan' (e.g. 为将来打算) or 'intend to' (e.g. 打算将来去英国) in English
A '打算' can be an 'intention' or a 'plan'
计划 means 'to plan' (v) ; 'plan' (n).
When you 计划 (plan) something, you are formulating a workable plan with at least some form of mental calculations, and the objective should be a specific one. For example, 政府計劃[十年內逐步削減赤字, 達到收支平衡]. Which is a very specific objective
A '计划' is a 'plan'
“计划” is more formal and “打算” is more used in oral language.
"计划" means : You have a goal and you create a plan to achieve that goal.
Example: “我计划去学习” (I want to study and I have a study plan)
"打算" means： You have a goal but you haven't take any actions.
Example：“我打算去学习” (I want to study, but It’s just a thought)
计划 vs 打算
Both can be used as verb and noun.
There is overlap in meaning for these two words.
计划 sounds more formal, implying you have deep thought on it and well planned, maybe you have made a list for things you intend to do, and you might have detailed schedule, budget and etc.
打算 is more colloquial or less formal. It's usually just rough idea about what you are going/wanting to do, and you might not have it well planned.
So, we say 周密的计划，but not 周密的打算. We tend to use 打算 in spoken when you are going to do something specific(not that complicated or important), like 我打算去逛街，我打算找个朋友聊聊天. We don't usually say 我计划找个朋友聊聊天 in this case, which sounds a bit pretentious I think.