What is the difference between a portmanteau and a kenning?

The words portmanteau and kenning come from different contexts and refer to different kinds of compounding. Kenning was first used in English by 19th century scholars trying to describe a feature of Old Norse and Old English poems: the use of periphrastic compound expressions instead of a simple description of a thing (OED). Here are a few examples that show the compounding at work (Wikipedia):

• sea => hron-rad (whale road)
• honor => weorðmyndum (worth of mind)
• sun => heofen-candel (heaven-candle)

Kennings often involve some kind of creative analogy, like imagining a sea as a road for whales, or the sun as a candle in the sky. Introductory literature courses often introduce kennings as a feature of Old English; if someone is talking about English in general, they are more likely to talk about a compound of some kind, like the noun compound "seat belt".

Portmanteau in English has referred to a specific kind of bag since the 16th century (OED). In the 19th century, Lewis Carroll adapted the term to refer to a word blending representative sounds from two or more words (CJR):

Well, 'SLITHY' means 'lithe and slimy. ' 'Lithe' is the same as 'active. ' You see it's like a portmanteau — there are two meanings packed up into one word.

So portmanteau don't just put two words together into a compound, but delete parts of the word to more fully blend them. So it's not smoke-fog but smog; it's not brother-romance but bromance.