「会いたくて」と「会いたい」の意味は同じですか？
What is the meaning of verb+kute like 食べたくて、飲みたくて、and how is it different from [tabetai] and [nomitai] which means "want to eat" and "want to drink" respectively....

Question

Answer

You can consider ～くて as te-form, which connect two sentences together. The tense is decided by the last verb.

あなたに会いたい。I want to see you. (Sentence finishes here.)
あなたに会いたくて、ここに来た。I wanted to see you(sentence continues), so I came here.

Sometimes, you may omit the second sentence and leave the rest to the implication.
あなたに会いたくて・・・（so I came.）

Answer

verb + て is used to connect 2 verbs. when a verb X is conjugated to 'want to X" form, the い becomes くて and it'll be followed by another verb.

the meaning is still the same