Hmm, I have a feeling that there will be various answers to your question since it would depend on the dialect. My family and I are southerners, so to me "a teacup" = "một tách (nhỏ)" and "a cup of tea" = "một tách trà". We do specify that "a teacup" or "a cup" in general is "một tách nhỏ (small)" and "a mug" is "một tách lớn (big)". Keep in mind that's just how my family and I say it.
The Vietnamese 'tr' combination sounds exactly the same as the English 'tr', NOT like the English 'ch'.
Try some of the following:
Trung tâm (center / centre) Trường học (school) Trẻ (young) Một bức tranh (a painting)
The Vietnamese 'ch' combination sounds the same as the English 'ch' in "church".
Chè (a kind of sweet dessert) Cha mẹ (parents) Cho (to give) Chu đáo (thorough)