For the definitions and differences of High/Sung/Low Mass with regard to the TLM, this recent thread may be helpful (esp. post 6)
As regards the candles: The common usage now (I think) in the TLM is 6 candles for a Solemn Mass, 4 candles for a Sung Mass and 2 for a Low Mass. However, the Sacred Congregation of Rites, which was entrusted with the liturgical interpretation and legislation, had certain further decrees dealing with this. So the rules determining the number of candles on the altar are
(1) For a solemn Mass 6 candles on the altar. This number is not actually givenby the rubrics, but inferred from the rubric on the incensing of the altar.
(2) In a Sung Mass, the number is not prescribed. Some places have 4- at one point 6 was common. The decree of the SCR only says : " Plures quam duae adhiberi possunt"
In a Missa Cantata for the Dead (de Requiem) 4 candles , at least are required, by decree of the SCR
(4) In a strictly private Mass of those who are not Bishops or Cardinals, only 2 candles can be used.
But in a Mass like a parish or community Mass, or on the more solemn feasts, or in a Mass celebrated instead of a solemn Mass or sung Mass (as might be the case on Sundays and feasts in certain places due to lack of clergy or choirs) according to custom, it was permissible according to a decree of 1857 to use more than 2 candles
(5) In a strictly private Mass celebrated by a bishop or Cardinal, on ordinary occasions, 2 candles suffice, but I think 4 was more common. 4 was required on solemn feasts. In a Mass not strictly private more than 4 could be used.
(6) 7 candles were required whenever the bishop celebrated a Pontifical Mass solemnly in his own diocese. This, I think, is the still the rule in the NO.