I know that giving rather strange rules which demand quite different analyses of similar-looking constructions can seem worrying / bewildering / infuriating. Perhaps if we look at near-paraphrases it will help a little (perhaps not):
2. I look forward to seeing you.
The string look forward is rarely used without the to (it would then be a less opaque idiomatic usage - don't look at what has happened in the past; look forward/s - and then ahead would probably be preferred anyway). (Google searches for "look forward to" and "look forward" -"look forward to" lend reasonable support to this claim.)
Look forward to has the fairly opaque (not too guessable from its component words) idiomatic meaning, eagerly anticipate. I'd say it has a unitary meaning (although in this case, I can only think of a two-word 'synonym', not a single word one - and perhaps 'anticipate quite eagerly' is closer in sense). Some would class the three-word string as a transitive multi-word verb (and possibly reclassify the to as a particle if pressed to parse individual words).
Notice that a noun as well as an -ing group could occupy the object space:
I look forward to seeing you.
I look forward to playing.
I look forward to the concert.
1. I want to see you.
Here, although there are again arguments for considering want to as a unit (He helped wash up / he helped to wash up; I want to go / je désire aller; But I want to!) there are considered to be more persuasive reasons for us to consider the to as more tightly bound to the base form of the following verb (to make a to-infinitive rather than the bare infinitive):
To see you tomorrow is impossible.
What do I want most? To see John.
I intend to see him tomorrow.
?/* Sorry, what did you say you intend?
Sorry, what did you say you intend to do?
*Sorry, who did you say you intend to?
Sorry, who did you say you intend to see?
*I intend to the concert.