「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

لا تفوّت فرصة تعلّم لغة جديدة وأنت مرتاح في منزلك. تصفّح مجموعتنا المختارة من مدرّسي اللغات ذوي الخبرة وسجّل في درسك الأول الآن!