Stemming is often executed as a set of rules from stripping all affixes--both derivational and inflectional--from a word, leaving its root. Lemmatization typically only removes inflectional affixes. Stemming is a much more aggressive version of lemmatization. Given what you want, it seems like you'd prefer lemmatization.
To compare the two, most lemmatizers are limited to a few rules for dealing with affixes to nouns and verbs in English---ed, -s, -ing, for example. There are a few irregular cases they have to handle, but with some training data, many are probably covered.
Stemmers are expected to dig deeper. As a result, the space of possible transformations they can make is bigger, so you're a lot more likely to end up with errors.
To see what's happening in your data, let's look at the specifics.
online -> onli: why on earth would this happen? Not totally sure on this one; there's probably some rule that tries to cater to words like medic-ine and medic-al, sub-mari-ne and mari-ne, imagi-ne and imagi-na-tion.
only -> onli, many -> mani: These seem particularly strange, but are probably more reasonable than the previous rule--especially in the context of dealing with verbs that end in -ed. If you're stemming the words denied, studied, modified, specified, you'll want them to be equivalent to their uninflected forms deny, study, modify, specify.
You could have a rule to transform each verb into the uninflected form, but the authors here chose to make the roots the forms ending in -i. To ensure that these match, -y endings had to be transformed to -i as well.
With a lemmatizer, you might get more predictable results. Since they only remove inflectional affixes, you'd get only, many, online, and thing, as you wanted. Both a good stemmer and lemmatizer can work well, but the stemmer does more stuff and therefore has more room for error.
