A monologue is a single person speaking as opposed to dialogue which is two or more, and when we say internal we mean in their head. Therefore an internal monologue is our character’s thoughts but precisely what we define as an internal monologue may vary.
For instance, we may say that if we’re writing first-person/subjective narrative then everything is internal monologue because it is all filtered through the character’s perspective. By everything I mean not simply internal debate but also the description of the environment, other people’s actions and anything else you can think of. The ‘I’ narrator gives us their opinion of everything whether they mean to or not.
A limited omniscient arguably does a similar thing because we are limited to that character’s perspective. However, we are more detached from their thoughts than the subjective narrator because, although we are limited to what they know, it is more clearly the writer telling us the character’s thought. It would be ‘Sam thought, Sam wondered,’ not ‘I thought, I wondered’. When it comes to description in this can give a sense of it being less the character’s opinion of the surroundings and more an impression of the authorial voice (the author’s opinion). This is part of the reason why limited omniscient is considered a more ‘reliable’ narrator than that of first-person, because there is less of a sense that we are listening to the character tell their own story.
In a third person narrative that is omniscient, not limited to a single character, therefore we wouldn’t consider the description of the environment as part of the internal monologue of the characters unless it is clear the setting is being described by the character. Otherwise it is assumed that the description comes from the authorial voice, which is assumed to be completely reliable unlike the subjective narrator. Therefore the internal monologue of the character would be considered the specific thoughts of the character. We may have a description of the setting and then we may have a statement of the character’s thoughts on the setting:
The fireplace was a large baroque design, wrought in plaster and decorated with gold leaf. Sam considered the whole thing very excessive.
The description of the fireplace is the authorial voice while the second part is Sam’s opinion of the fireplace, this would be considered part of Sam’s internal monologue, we may expand upon Sam’s thoughts in a full length description or we may not but it being Sam’s thoughts distinguished it from the authorial voice. In an omniscient narration we may also switch between multiple characters thoughts/internal monologues which happens in limited omniscient but generally is more distinct than in omniscient. By which I mean that in omniscient we are freer to move between characters as we choose but limited omniscient usually requires that we have a section or chapter break to do so, we don’t usually do it between paragraphs.
How much or how little we rely on internal monologue depends upon stylistic choices rather than set rules while there may be places we can trim any excess such as repetitions.