"Rightsizing" is a euphemism. It is an evasive way of talking about "downsizing" to make it sound nicer. "Downsizing" means "making the size of the workforce smaller," i.e. laying people off. "Rightsizing" is usually deceptive. It means "to make the workforce the right size," i.e. the size it ought to be. This sounds nicer for two reasons. First, it carries the clear idea of an improvement. Second, it carries the idea--almost always false--that the "right" size could be any number, not necessarily smaller, but possibly larger, whatever is the "right" size. It doesn't fool employees but perhaps it makes employers feel better about what they are doing.

They are both corporate jargon for telling normal people that they are losing their jobs.

I found this explanation on a website that deals with small businesses. At least in the context of business these seem to be a good clear definitions: "Downsizing involves reducing the number of employees a company has to increase profitability and reduce redundancies. On the other hand, rightsizing is about more than reducing the number of employees. It's about getting the organization to the right size for its new business objectives." I would just add that in the UK at least, 'downsizing' is commonly used to describe the situation when people sell a larger house to move into a smaller house, either because it's too big, expensive to run or difficult to manage. It is relatively recent in use (nobody used this expression when I was young...). I suspect it's probably a more fashionable way of avoiding having to say something like "I can't afford my big house anymore." 🙂