Ah. Those are different verb forms of szeret. Szeret is the form you'll find in dictionaries (the 3rd-person singular indefinite conjugation, "he loves"), so I'm using this form to talk about the verb, generally.
Szeretni is the infinitive form, in English "to love" or "to like", like you correctly assumed. This form is mostly used in conjunction with another verb, because only one verb per clause should be conjugated, for example:
- Nem tudok szeretni. - I cannot love. (Tudok / "can" is the conjugated verb, while szeretni / "love" is in the infinitive form.)
- Akar szeretni. - He wants to love. (Here you can see the full infinitive in English, including the "to".)
In the above sentence, szeretsz is conjugated and táncolni is infinitive.
Szeretnél, on the other hand, is in a different mood, the conditional. All conditional forms have a suffix containing -ne/-né- or -na/-ná-, so they're relatively easy to pick out. Szeretnél (2nd-person singular indefinite conditional) just means "you would like". "Szeretnél táncolni?" - "Would you like to dance?"