What is a lean mass-up (lean bulk)?

In one line

A lean mass-up is a way to build muscle by eating only a little more than usual and gaining weight slowly, so body fat does not rise more than needed.

What is a lean mass-up (lean bulk)?
How is it different from simply eating a lot to bulk up?
At the gym you may hear 'I'm doing a lean mass-up these days.' People use it to mean building muscle while gaining less fat. How is it different from a bulk-up, where you simply eat a lot?
In one line
Eating a little more and growing slowly
A lean mass-up is a way to build muscle by eating only a little more than usual and gaining weight slowly, so that body fat does not rise more than needed. It is built on doing strength training at the same time.
What the words mean
'Raise your size without extra fat'
In English, 'lean' means 'without much fat', and 'mass' means 'a lump' or 'a large amount'. 'Up', meaning 'to a higher level', is added. Put together, it means 'raise your size without extra fat'.
Background
Maintenance calories and a calorie surplus
If the calories you eat equal the calories your body uses, your weight stays the same. That amount is called 'maintenance calories'. Eating more than that, so energy is left over, is called a 'calorie surplus', and your weight rises by the amount left over.
Why only 'a little' more
Muscle can only grow so fast
There is a limit to how fast new muscle can be added. So even with a large calorie surplus, muscle does not grow that much more, and the leftover energy is stored mainly as fat. A lean mass-up keeps the surplus small to cut down that leftover share.
How slowly
25-0.5% of body weight per week
The pace researchers suggest is about 0.2-0.35 kg per week for a person who weighs 70 kg. The longer someone has trained and the more muscle they already have, the slower they are advised to go.
What research found
Eating more did not grow more muscle
One study of people who had already been strength training for a while compared a group that ate a little above maintenance with a group that ate a lot above it, while both did strength training. Muscle thickness did not differ between the groups. Instead, the faster a person gained weight, the more the fat layer under the skin grew.
How it relates to bulking
One way of bulking up
'Bulking up' is the broad word for eating a lot and training hard to get bigger. A lean mass-up is one way of doing it that keeps the calorie surplus small to limit fat gain. Both raise body weight.
How to adjust
Watch the weekly average weight
Body weight goes up and down even within a day. So people weigh in daily or several times a week and look at how the weekly average changes. If the average rises too fast, they eat a little less; if it barely moves, they eat a little more.
Common myth / Does a lean mass-up add only muscle and no fat?
It limits fat gain; it does not make it 0
A lean mass-up still raises weight with a calorie surplus, so not all of the added weight is muscle. In research, too, the more weight a person gained, the more the fat layer under the skin grew. The goal is not '0 fat gain' but 'no more fat than needed'.
Summary
A small surplus, a slow gain
A lean mass-up is a way to build muscle by eating only a little more than usual and gaining weight slowly, without adding more fat than needed. It is not a way to gain no fat at all. Related terms: bulking up, calorie surplus, cutting.