Engl: to suckle, to suck
You need a tube that is connected at one end to a chamber with a pressure that is lower than on the other end of the tube. Then this lower pressure will cause fluids (liquids and gasses) to move into the chamber where the lower pressure is.
This is the principle of a »Staubsauger« (vacuum cleaner) and of a »Saugpumpe« (lift pump). And it is the same principle that you use when you drink soda through a straw, where your mouth is the chamber with low pressure. And is also is the principle that newborn mammals use when they drink milk from their mother's udder; in which case the nipple will be the drinking tube.
Also, when you form a ring with your lips, with a very small opening, and when you then breath in, so that you hear that typical noise, you say
Luft einsaugen = to "suck" in air.
Engl: to suck
This is somethings machines can't do, because you need a tongue to do so. »Lutschen« means, that you have something in your mouth and move it between tongue and the roof of your mouth to make it melt, deliquesce or dissolve. You again and again swallow the molten or dissolved parts and keep moving the hard thing in your mouth until it completely has gone.
Typically you have hard candy, chocolate or similar sweets in your mouth when you do what is called »lutschen« in German. You don't need low pressure for »lutschen«, but you need to have a mouth and a tongue.
Engl: to lick
This is lutschen, but outside of the mouth. You have something that can melt or dissolve but that's too big to completely put it in your mouth. Think of ice cream or a big lolly.
So, »lutschen« is much more like »lecken« than »saugen«.
- Saugen is always about producing low pressure.
- Lutschen and lecken are both about using your tongue.
And all three verbs also exist with a sexual connotation.
- »Lecken« is mainly cunnilingus, but also all other activities where you move your tongue over somebodies skin.
- »Lutschen« is sometimes used to describe fellatio, but the verb »blasen« (to blow in it's meaning »to make bigger«) is more commonly used.
- »Saugen« is only used to describe fellatio when you really create low pressure in your mouth, otherwise its »blasen« or »lutschen«. But of corse you also can saugen on other parts of someones body (finger, nipples, toes, ...), but if you use this word, it's always meant to create low pressure in your mouth.