The concept you are referring to is known as relativistic mass increase or mass dilation in special relativity. According to Einstein's theory of special relativity, as an object moves faster and approaches the speed of light, its relativistic mass increases. This means that the mass of an object appears to be greater when it is in motion compared to when it is at rest.
It's important to note that the notion of relativistic mass has fallen out of favor in modern physics. Instead, physicists now typically use the concept of invariant mass, also known as rest mass or simply mass. The invariant mass of an object is a fundamental property that remains the same regardless of its motion.
In the context of gravitational fields, the increase in mass is not related to relativistic mass dilation. In general relativity, the theory that describes gravity, mass and energy curve the fabric of spacetime, creating what we perceive as a gravitational field. However, this does not lead to an actual increase in an object's mass. The mass of an object remains constant regardless of its position in a gravitational field.
In summary, the increase in mass due to relativistic effects is a concept from special relativity and is not directly related to the mass increase in a gravitational field as described by general relativity.