The words are almost identical in meaning. Restrain means hold back from behind, constrain means hold back by setting barriers in the way ahead. A dog on a leash is restrained, a dog in a cage is constrained. LouiseT on EnglishForums
Startups often make progress when constrained. The most common constraint is lack of resources, usually money. But there are other common ones too: lack of experience, lack of connections, lack of knowledge, to name a few. They overlap of course.
Constraints usually lead to intense focus on a subset of a larger problem, and when that works out, serendipitous discovery. Constraints help you break through the paradox of choice.
This is why raising too much money as a startup can be counter-productive early on. You're reducing your constraints, and counter-intuitively that can lead to less success for all the reverse reasons. You now have a paradox of choice.
The money is actually restraining you, if you let it. All of a sudden you don't have the excuses of constraints to move fast, and things often slow down.
Big companies are even more restrained. The most common restraint is existing product lines, again usually money (but in this case not killing revenue). There are other common ones too: existing processes, existing hierarchy, existing infrastructure, to name a few. They again of course overlap.
By all means add constraints on yourself and your company, but be very wary of restraints.