
fettig
greasy
Covered, soaked, or smeared with fat or oil.
Nach dem Essen der Pommes hatte ich ganz fettige Finger.
After eating the fries, my fingers were completely greasy.
greasy / oily
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greasy
Covered, soaked, or smeared with fat or oil.
Nach dem Essen der Pommes hatte ich ganz fettige Finger.
After eating the fries, my fingers were completely greasy.

oily
Describes skin or hair that produces an excessive amount of sebum and therefore appears oily or shiny.
Ich muss meine Haare waschen, sie fühlen sich schon wieder fettig an.
I need to wash my hair; it already feels oily again.

greasy
Informal term for foods that contain a lot of fat and are therefore very rich.
Der Braten war zwar lecker, aber auch ziemlich fettig.
The roast was tasty, but also pretty greasy.
The adjective 'fettig' (greasy/oily) is derived directly from the noun 'das Fett' (fat). The ending '-ig' turns the noun into an adjective and means 'having the quality of something.'
Die Soße war mir etwas zu fettig.
The sauce was a bit too greasy for me.
Do not confuse 'fettig' (greasy/oily) with 'fett' (fat). A person or animal can be 'fett' (overweight), but their skin or hair is 'fettig' (oily). 'Fettig' describes an oily surface.
Meine Haut im Gesicht ist leider sehr fettig.
Unfortunately, the skin on my face is very oily.
In connection with personal care, 'fettig' (oily) is almost always used for 'fettige Haut' (oily skin) and 'fettige Haare' (oily hair). It describes a condition that many people want to avoid.
Es gibt spezielle Shampoos für fettiges Haar.
There are special shampoos for oily hair.
When food is described as 'fettig' (greasy), it is often informal and has a slightly negative meaning. It implies that the food is very rich or perhaps even unhealthy.
Das Essen in der Kantine ist oft ziemlich fettig.
The food in the cafeteria is often pretty greasy.
fat / bold
Both words can describe a very rich dish. „Fett“ mainly emphasizes the high fat content, while „fettig“ can also emphasize an oily or greasy feel. When discussing the composition, „fett“ is appropriate; when describing the feel or appearance, „fettig“ is often more precise.

Die Pizza ist so fettig, dass ihre Oberfläche vor Öl glänzt.
The pizza is so greasy that its surface is shining with oil.
Die Pizza ist wegen des vielen Käses sehr fett.
The pizza is very fatty because of all the cheese.