Usually ‘Mülleimer’ is a smaller size garbage can that is kept in kitchen or floor, sometimes outside in parks or other public places like the photo below.

Der Mülleimer - garbage can (Image credit: Thomas, Source: Flcikr, CC BY-SA 2.0)
whereas ‘Mülltonne’ are larger size garbage containers outside houses where wastes from ‘Mülleimer’ are dumped and normally municipal garbage trucks collect them for recycling and dumping. Here wastes are sorted according to their types like plastic wastes in containers marked only for plastic wastes, marked containers for biological wastes, containers for papers only etc.

Die Mülltonnen - garbage containers (Image credit: onnola, Source: Flickr, CC BY-SA 2.0)
Some other words related to waste:
der Müll – waste
der Eimer – bucket (pl. die Eimer)
der Beutel – bag, sac
der Müllbeutel – garbage bag
die Tüte – bag
die Mülltüte – garbage bag
die Mülldeponie - landfill, garbage dump
die Müllhalde – landfill, garbage dump
der Papierkorb – waste paper busket
der Restmüll – residual waste
der Abfall – waste, garbage (pl. die Abfälle)
Wo sind die Mülltonnen? – Where are the garbage containers?
Wo stehen die Mülltonnen? - Where are the garbage containers?
Die Mülltonnen stehen draußen, direkt vor dem Haus - The garbage containers are outside, directly in front of the house.

Die Mülldeponie - landfill/municipal waste dumping site (Image credit: Bill McChesney, Source: Flickr, CC BY 2.0)
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