A potato peeler is a metal blade attached to a handle that is used for peeling certain types of fruits and vegetables: potatoes, carrots, apples, pears, to name but a few. It is however not suitable and will not work on vegetables such as celeriac or kohlrabi or citrus fruits such as oranges & lemons. For these, a normal sharp knife is better and more preferable. The blade of the peeler is often curved so it can also be used to remove the cores from fruits such as apples. It may also have a serrated/sharpened ring on its its tip to facilitate coring.
A modern counterpart is a speed peeler. These can be razor sharp so take great care when using them. Rather than use a lemon zester to remove the zest from citrus fruits, use a speed peeler to remove large shavings of zest and then chop these into smaller pieces with a sharp knife. The seems to be much more effective than using a purpose built zester. They can be used on thick skinned veggies like celeriac and kohlrabi but it may require many passes over the same area and it may skip so much that you will in the end resort to using a sharp knife on a chopping board. I have never got on with these peelers until I bought and OXO Good Grips one and it is brilliant. They are available from Lakeland.
A mandoline is a kitchen utensil used for slicing and cutting juliennes; with proper attachments, it can make crinkle-cuts. It consists of two parallel working surfaces, one of which can be adjusted in height. A food item is slid along the adjustable surface until it reaches a blade mounted on the fixed surface, slicing it and letting it fall.
One of the advantages of using a mandoline is that the slices will be uniform in thickness, which is important with foods that are deep-fried or baked (e.g. potato chips), as well as for presentation. Another advantage is that the slices can be very thin, with much less effort than would be required cutting with a knife or other blade.
This is a dangerous utensil and food preparers may choose to wear a metal glove on the pushing hand.