Suppose I tell something to my companion and I want to make sure he understands me. I thought I may simply ask "Do you understand me?". But recently I heard that in such cases I should ask "Does that make sense?" instead. Is this true? Which option is appropriate to use in business communication?
In many contexts the two sentences are equivalent.
In some situations, "Do you understand me?" carries overtones of superiority, intimidation, etc. Correspondingly, in some other situations, "Does it make sense?" implies submissiveness, uncertainty, etc.
In a business communication I would avoid using either form. Partly because of the possiblity the recipient might pick up on either of the above overtones (which presumably you wouldn't intend), but mainly because I feel they are both a bit informal for the context.
Better by far to say something like Please do not hesitate to ask for clarification if required.
I think there's a small difference.
"Do you understand me?" is usually confirming, in a straightforward manner, whether somebody understands the facts/argument of what you have said.
"Does that make sense?" (usually with "that", at least in UK English) can mean something similar, but is a more loaded question, implying that the other party should or has an obligation to understand what was said, and that if they don't, they are in some way stupid or disobedient. If the person saying this is your boss, they're not really enquiring about your ability to follow their argument, but effectively saying "Now do as you're told".
"Do you understand me?" seems very rough because of "me". I would change it to "do you understand?". By asking this it seems that the listener might not understand, which implies that you are not completely equal. This question sort of fits better if you are speaking to someone who doesn't really speak your language. So the understanding means that you might not actually be capable of understanding.
"Does that make sense?" Is a nice way of asking if you are making yourself "understood" But more towards a politeness as @Henry says. I would use this option over the other one any day. And I think that is the best you can do.
I would say that both have their tendency to offend. Literally, questions are questions; however, we are talking now about sociolinguistics and implied verbiage. Regarding "Does that make sense?"— is still a little offensive and condescending. Typically used in verbiage to a child from a parent, it seems that this has become prevalent in the workplace these days. Think about how the respondent might answer, yes or no, and if no, then you might have just put the word 'idiot' behind the phrase. "Does that make sense, idiot?"
In American english, many will use this phrase in a disciplinary manner to advise or reinforce to the listener that no argument or failure to comply will be tolerated. ie: "Do not do that again. Do you understand me?" Since the phrase is frequently used in this manner, it takes a negative or angry connotation in general speech and will frequently draw an unintended negative response. If making a genuine request to an equal to confirm that you are being understood I would more likely choose a phrase like "Am I making sense to you?", or more casually "Do you get me?"
I generally go with a simple:
Is this explanation okay..?
As it sounds neutral and encourages the receiver to provide feedback.
If I used pronouns while asking for feedback, like "Did you understand..", "Did I explain this..", .. it generally makes the receiver feel like you might take their feedback negatively or take offense if they were not able to understand.