"While" and "As" conveying a continuous aspect

Question

I have noticed that "While" and "As" trigger a continuous meaning of the verb which, however, is used in the default form, so to speak. For example,

I am thinking of my work as/while we speak now.

Basically, "we speak now" means that we are speaking right now, hence, the Present Continuous could be used here. But I see that it is very often when the Present Simple is used. Now my question is whether the meaning remains the same regardless of whether we use the Present Simple or the Present Continuous.

Do the following sentences mean the same?

You may say embarrassing things while you are coming out of anesthesia.
You may say embarrassing things while you come out of anesthesia.

If your car jerks while you are coming to a stop, it might mean that your brakes are in bad shape.
If your car jerks while you come to a stop, it might mean that your brakes are in bad shape.

What are you doing while I sit here watching waves?
What are you doing while I am sitting here watching waves?

Answer 1

Yes, each of your example pairs mean the exact same thing.

Answer 2

IMO,

The conjunction 'while' is used to talk about something happening during particular time. And when anything happens during time, it has two ends -beginning and end. So, if a bomb blasts while you were in the market, it means the blast happened in between two points of time - when you entered in the market and when you came out. While, for this reason, seems to be common with present continuous as compared to present simple.

The BBC talks about it:

*...while as subordinating conjunctions to introduce adverbial clauses of time. They mean during the time that and indicate that something is or was happening when something else occurred.*

Let's take your first example:

You may say embarrassing things while you are coming out of anesthesia. The 'saying' of embarrassing things is happening during the time the person is coming out of anesthesia. This said, the process is continuous. On the other hand, you come out gives a bit flair of the process being completed or the things in general, regular way.

The BBC's example makes it clearer:

The prisoners escaped while the prison warders were eating their lunch.

What were warders doing? They were eating their lunch. Changing were eating into eat won't look that proper. That's because it may talk about escaping happens with a regular process to eat their lunch. The simple present in the first clause will then make sense.

The prisoners escape while the prison warders eat their lunch!

Another example could be...

My cat sits beside me while I eat my meal.