Thinking before speaking is filtering out anything where its cons for being said outweigh its pros. It has nothing to do with whether or not you think something is true or false. It doesn't even need to be a truth statement.
Self-censorship is a different name for the same concept. The only reason I avoid saying certain things in certain contexts is because I believe there will be negative backlash that outweighs any possible gains in communicating my thought.
I don't quite agree with your argument.
In the literal sense thinking before speaking is just that. It can lead to you rephrasing your thoughts multiple times before you find a way to convey what you want to say in such a manner, that a listener is able to understand you.
Of course, it can also lead to an act of self-censorship if the cons outweigh the pros.
Originally, the word "censorship" was not used in a context where this consideration was done, be it thoughtfully or at all.
So while defining self-censorship like you do is certainly possible, it is inconsistent with other meanings of censorship, where multiple parties may be involved.
It is up to you, of course, to expand its meaning to "thinking before speaking", but other people seem to mean similar, but not quite equal, things with these words. Unifying them by using a weaker definition (Although I don't believe that "think before you speak" is well defined at all) will only lead to a loss of information that facilitates misunderstandings. I'd rather know that I might be misunderstanding something instead of having peace of mind with a definition that is so broad it becomes meaningless.
Thinking before speaking is filtering out anything where its cons for being said outweigh its pros. It has nothing to do with whether or not you think something is true or false. It doesn't even need to be a truth statement.
Self-censorship is a different name for the same concept. The only reason I avoid saying certain things in certain contexts is because I believe there will be negative backlash that outweighs any possible gains in communicating my thought.