Chinese and Burmese both belonging to the Sino-Tibetan language family does not mean they're actually similar to each other. Can Iranians and Indians speak Italian or French? After all, Hindi and Farisi are also Indo-European languages.Awesome writing. One interesting aspect about this situation is that most of the ethnic groups in Myanmar including the Bamar are speakers of Sino-Tibetan language family. So, they should be kinda close to Chinese language compared to Thai or Vietnamese, who are from a different language family.
So, it might be possible over time for China to takeover Myanmar. Or atleast make Myanmar a client state. Because of the closeness in Language family, it might be easier to control these lands. If China ever becomes the dominant power in asia then taking over myanmar could end China's Malacca Dilemma for good and allow China access to the Indian Ocean. A myanmar full of Chinese naval, air and army bases could be strong deterrent against any blockade attempts by US or India.
Again this is probably not happening in this century because China will be busy fighting the US in the eastern pacific for a long time. But in a long term scenario, Taking over Myanmar which is a weak country full instability might be easier than other countries in the neighborhood.
Language families indicate historical relationships and descent. It has nothing to do with how close they are to each other today. And by historical relationship, it can be up to 5000+ years ago. For reference, there's national European languages that discovered writing only ~500 years ago.
Example: Vietnamese has closer grammar to Chinese than Burmese does. For example, just like all variants of Chinese, Vietnamese is an with no case or inflection. In contrast, while
The only reason there are Chinese speakers in Myanmar is because the Chinese speakers are literally Chinese. That's it. There's almost 0 Bamars who speak Chinese.
Burmese identify far more with India and Thailand than with China, and view their language, culture and ethnicity as having nothing to do with Chinese. This is in contrast to Vietnamese who often readily admit they're mixed with Chinese and their language is deeply influenced by Chinese to the degree where it's hard to even separate native Vietnamese from Chinese loanwords.
This isn't saying that Vietnam should be part of China but the absurdity of 5000 year old historical linguistics to estimate how easy it would be to "take over" a country.