What is the difference between:
ni pensas malsame | ni pensas malegale | ni pensas diverse | ni pensas alie
all more or less the same with different nuances? If i had to guess I would say "alie" emphasizes rather the contrast while the others rather emphasize the diversity. Who can tell more exactly?
If you want to make this phrase with an adjective in the nominative case, it have to be plural, since the subject is plural. So ni pensas aliaj (we, who are other [than somebody just mentioned], think).
There are several interpretations of this slogan. If they meant a flat adverb (adverb, but without the “-ly” ending) then it'd be pensu alie; if the adjective was meant then it's pensu alia / pensu aliaj (but it doesn't make much sense); and if we believe Steve Job's official biography and see it as a noun then it's hard to translate, but would have to be pensu pri alio / pensu pri alia / pensu „alio”.
Also, normally company names aren't translated by their meaning, but esperantised phonetically and made into a noun by sticking the “-o” ending, just to make the pronunciation and derivation clear. So “Apple” is either left in its original form or esperantised as Aplo.
As a rule of thumb: adjectives (a-vortoj) are used to qualify nouns, while adverbs (e-vortoj) are used to qualify verbs and adjectives. You can think of adjectives as answers to the question kia? (‘what kind of?’) and adverbs as answers to the question kiel? (‘how? in what manner?’).
In the sentence “we think otherwise” the word “otherwise” describes the manner in which we are thinking, and so as a description of the verb “to think” it needs to be an adverb alie.
Compare those two examples:
- Ili kantis laŭte kaj ni kantis alie. — ‘They sang loudly and we sang differently.’
- Ili kantis tiun kanton kaj ni kantis alian. — ‘They sang that song and we sang a different one.’
In the first sentence you say ni kantis alie, because alie qualifies the verb kantis by describing the manner in which we sang — it was a different one than laŭte (‘loudly’). In the second sentence you say ni kantis alian, because alian qualifies the noun kanton (which was ellipsed to avoid repetition) by describing which song we sang — it was a different one than tiu (‘that one’).
You confused the general adverb ending -e with the second halves of the pro-forms of manner -el.
General word endings (such as -o, -a or -e) can always be swapped or added to change the meaning of the word. For example you can add the adverbial ending -e to the root ali- and thus create the word alie meaning ‘differently, otherwise’. Alternatively you can think of this process as taking the base form, which in case of the root ali- is the adjective alia (‘other’), and swapping the adjectival ending -a for the adverbial ending -e.
The correlatives in Esperanto is something we call a closed word class, because no new words of that type can be created (so like pronouns or articles — only one article in Esperanto, to be precise — and very much unlike nouns, verbs, adverbs or adjectives). And so although they do have a neat pattern of regular first and second halves forming a table, the components of the correlatives cannot be used outside of this word class. Since ali- is just a regular word root, you cannot attach to it the second half of the pro-forms of manner -el.
Additionally, please notice that the adverbial ending -e covers much more semantic space than just the pro-forms of manner. Among other things it can also describe location (hejme ‘at home’, like the pro-forms ending with -e), quantity (multe ‘a lot’, like the pro-forms ending with -om), time (matene ‘in the morning’, like the pro-forms ending with -am) or reason (senkaŭze ‘without reason’, like the pro-forms ending with -al).