Katara:

From the comics, we know that Korra has known Katara since early childhood. They seem to have a familial relationship, meaning no stuffy titles are needed.

Tenzin:

In the actual series, Korra initially does address Tenzin as "Master Tenzin."

KORRA: Master Tenzin, I'm so glad you're here. I can't wait to get started.
_{The Legend of Korra, Book 1: "Air", episode 1: "Welcome to Republic City"}

She gives this up later in the episode, though. I would chalk that up to various established personality and context differences between Aang and Korra. Aang was raised as a monk in a very traditional, respect-oriented environment, seen as somewhat archaic even by the time of the original show. For example, see how he calls Zuko "Sifu" against Zuko's wishes. Korra is generally more headstrong and was raised in a less rigid, more modern environment. She also soon had a closer relationship with Tenzin than Aang did with Pakku. She lived with Tenzin and his family for an extended period of time, while Aang was forced to move on from Pakku quickly.

Katara:

From the comics, we know that Korra has known Katara since early childhood. They seem to have a familial relationship, meaning no stuffy titles are needed.

Tenzin:

In the actual series, Korra initially does address Tenzin as "Master Tenzin."

KORRA: Master Tenzin, I'm so glad you're here. I can't wait to get started.
_{The Legend of Korra, Book 1: "Air", episode 1: "Welcome to Republic City"}

She gives this up later in the episode, though. I would chalk that up to various established personality and context differences between Aang and Korra. Aang was raised as a monk in a very traditional, respect-oriented environment, seen as somewhat archaic even by the time of the original show. For example, see how he calls Zuko "Sifu" against Zuko's wishes. Korra is generally more headstrong and was raised in a less rigid, more modern environment. She also soon had a closer relationship with Tenzin than Aang did with Pakku. She lived with Tenzin and his family for an extended period of time, while Aang was forced to move on from Pakku quickly.

The original show actually sets the precedence that familiarity can trump formality. Aang initially calls Toph and Zuko "Sifu" because he was (re)introduced to them as teachers. He doesn't do this with Katara, who he befriended prior to her teaching him.

KATARA: Hey, you never called me Sifu Katara. _{Avatar: The Last AIrbender, Book 2: "Earth", episode 9: "Bitter Work"}

Katara:

From the comics, we know that Korra has known Katara since early childhood. They seem to have a familial relationship, meaning no stuffy titles are needed.

Tenzin:

In the actual series, Korra initially does address Tenzin as "Master Tenzin."

Master Tenzin, I'm so glad you're here. I can't wait to get started. - Korra, "Welcome to Republic City"

She gives this up later in the episode, though. I would chalk that up to various established personality and context differences between Aang and Korra. Aang was raised as a monk in a very traditional, respect-oriented environment, seen as somewhat archaic even by the time of the original show. For example, see how he calls Zuko "Sifu" against Zuko's wishes. Korra is generally more headstrong and was raised in a less rigid, more modern environment. She also soon had a closer relationship with Tenzin than Aang did with Pakku. She lived with Tenzin and his family for an extended period of time, while Aang was forced to move on from Pakku quickly.

Katara:

From the comics, we know that Korra has known Katara since early childhood. They seem to have a familial relationship, meaning no stuffy titles are needed.

Tenzin:

In the actual series, Korra initially does address Tenzin as "Master Tenzin."

KORRA: Master Tenzin, I'm so glad you're here. I can't wait to get started.
_{The Legend of Korra, Book 1: "Air", episode 1: "Welcome to Republic City"}

She gives this up later in the episode, though. I would chalk that up to various established personality and context differences between Aang and Korra. Aang was raised as a monk in a very traditional, respect-oriented environment, seen as somewhat archaic even by the time of the original show. For example, see how he calls Zuko "Sifu" against Zuko's wishes. Korra is generally more headstrong and was raised in a less rigid, more modern environment. She also soon had a closer relationship with Tenzin than Aang did with Pakku. She lived with Tenzin and his family for an extended period of time, while Aang was forced to move on from Pakku quickly.

Katara:

From the comics, we know that Korra has known Katara since early childhood. They seem to have a familial relationship, meaning no stuffy titles are needed.

Tenzin:

In the actual series, Korra initially does refer to him as "Master Tenzin."

Master Tenzin, I'm so glad you're here. I can't wait to get started. - Korra, "Welcome to Republic City"

She gives this up later in the episode, though. I would chalk that up to various established personality and context differences between Aang and Korra. Aang was raised as a monk in a very traditional, respect-oriented environment, seen as somewhat archaic even by the time of the original show. For example, see how he calls Zuko "Sifu" against Zuko's wishes. Korra is generally more headstrong and was raised in a less rigid, more modern environment. She also soon had a closer relationship with Tenzin than Aang did with Pakku. She lived with Tenzin and his family for an extended period of time, while Aang was forced to move on from Pakku quickly.

Katara:

From the comics, we know that Korra has known Katara since early childhood. They seem to have a familial relationship, meaning no stuffy titles are needed.

Tenzin:

In the actual series, Korra initially does address Tenzin as "Master Tenzin."

Master Tenzin, I'm so glad you're here. I can't wait to get started. - Korra, "Welcome to Republic City"

She gives this up later in the episode, though. I would chalk that up to various established personality and context differences between Aang and Korra. Aang was raised as a monk in a very traditional, respect-oriented environment, seen as somewhat archaic even by the time of the original show. For example, see how he calls Zuko "Sifu" against Zuko's wishes. Korra is generally more headstrong and was raised in a less rigid, more modern environment. She also soon had a closer relationship with Tenzin than Aang did with Pakku. She lived with Tenzin and his family for an extended period of time, while Aang was forced to move on from Pakku quickly.