This question was asked by a new student who had before practised in another lineage for about 10 years. I was taken aback and flabbergasted. My main thought was: "Really? You are asking me this kind of question?" And found it difficult to answer properly.
There are two things which perplexed me. The first was that there seemed so little cultural understanding after someone had practised the style for 10 years. And it wasn't his fault, but his previous teachers had clearly wanted him to have no proper cultural knowledge. Secondly it was in an unintended way derogatory towards my lineage, because I knew he came from a lineage where everybody refers to their head teacher as "GRANDMASTER", like he is the only one out there. So obviously asking me if my teacher was now considered a master or a grandmaster clearly put him below the teacher being referred to as "grandmaster". From a marketing side I do understand the endeavor to try and put one man above everyone else if you can associate yourself with that person. It has happened all over the world in a lot of organisations, religious, political, sectarian, whatever. But we don't have to approve of it.
What is a Taijiquan master anyway?
The term "master" has very different connotations in the Western world. In German we would usually think about craftsmanship when we hear the term "Meister". So in medieaval times there were guilds and the title of "master" was meant to limit the amount of people who could follow a profession, but also to ensure the quality of the craftsmen as they had to go through some apprenticeship before. From my students in the USA I heard that the term "master" has quite different connotations because of US history and to my knowledge it is quite often associated with racial injustices (please correct me if I am wrong!). In German we would even use the English term "master" to refer to the respective events and would not use our German term. In Italy again the term "maestro" means also teacher, at least how I heard it from my Italian students. For them the connotation is entirely different and also quite down to earth. So there are quite a lot of different connotations associated with the term which we should be aware of in the West.
In Kungfu (in Pinyin written gongfu) of course the term evokes a different image again. Originally it came into use as a sort of approximation of the Chinese term "shifu".
The terms shifu, shimu, laoshi and more
In China, if you have gone through the "baishi" ceremony this means the that you have officially reconized your teacher as your "teacher-father" shifu. Then you have been accepted into the lineage of the respective teacher and can claim to continue that line's teachings. That means you can openly say who is your teacher and vice versa, plus the ceremony fosters commitment and opens access to the knowledge of the tradition. Not more but also not less. Whether you train well or not and whether you can acquire gongfu naturally still depends on your own enthusiasm, training intensity and talent. Also how exactly the relationship evolves or how difficult it is to become a disciple can vary somewhat from teacher to teacher.
Before one has been accepted, the teacher is usually called "laoshi", meaning teacher in a more general term. In the West teachers sometimes call themselves "masters" or even "grandmasters" as if it was some official title. In China, however, people generally address each other with a salutation that reflects the relationship status (brother, sister, aunt, teacher, etc. pp.). Thus the "teacher-father" (shifu) is also not a title in Chinese, but a relational term, depicting your relationship to the teacher. Similar to how you would adress someone in English as "aunt", "uncle" etc. This applies to the Chinese martial arts in Northern China (and thus Taijiquan tradition) as far as I know, in the South this can vary a bit and the term shifu seems a bit more common in an everyday kind of sense.
Usually I don't care too much about the use of any of those terms and also other approximations as these things are always a bit difficult across languages. But if someone uses any of those terms to claim superiority (like "my teacher is a grandmaster and yours a master") over others AND spreads misinformation (like "call me master XY as that is my official title") I think things should be clarified. To my mind credible teachers should not foster ignorance and exploit it for their own benefit or use it to look down on others. Rather they should help to spread information and cultural understanding. With a proper understanding of the context people can use whatever address they want to choose and which they think is most appropriate.
Is there a specific etiquette in Taijiquan?
In my experience the etiquette can vary widely in different schools and traditions. Usually it does not seem too strict in the Chinese Martial Arts. How I experienced it students and teachers treat each other in a friendly and normal manner. There is no bowing nor any militaristic atmosphere. Of course, etiquette has in the past always been adapted firstly by individual teachers and secondly according to the prevalant zeitgeist. There were times in the past where the baishi ceremony was completely forbidden, for example when Chinese emperors feared revolts in which martial artists might participate.
To me it seems sensible that there is a good mutual understanding and normal respect for the other person, without which martial arts cannot be developed properly. You need a certain amount of trust when you train together, especially when training potentially damaging movements, something martial arts are about per se. I believe there are some guidelines beneficial for personal development, e.g. the correct effort in training, the insight into why one is training and the realistic consideration of one's own abilities, a basic cooperative attitude which allows serious training and respect for the teacher, for one's students / disciples, one's classmates and even respect for oneself. These guidelines are not meant to be overly exaggerated or artificial but they represent rather normal social norms.
Here is a nice video Will from Monkey Steals Peach made explaining the teacher - student relationship from his perspective: