Don't listen to what they say. That ''rap is more like rhyming and hip hop is mostly singing'' - is not true.
Rap is basically words recited rapidly and rhythmically which usually rhyme, over an instrumental backing.
While Hip-Hop is the music genre which has rapping in it.
There are many music genres which have rap in them, the main ones Hip Hop and RnB
Hip Hop (which is the main one and is basically rapping over a continuous instrumental beat)
RnB, which stands for Rhythm and Blues is pop music and singing (usually at the chorus) with rapping at the verses. It's more ''melodical'' than hip hop.
Other sub-genres which have rap are:
hardcore hip hop, gangsta rap, ghetto rap, hip pop, rap rock and so on, I can spend an hour listing them out.
So let's recap:
Rap is the type of singing - rhyming words rapidly in a rhythm over a beat (or without a beat). Rap is not a music genre, however people call all music genres which contain rapping, Rap, just like Hip Hop.
Hip-Hop is the music genre which has rapping in it.
(Extra info: Hip Hop artists are called rappers because that's what they do, obviously. They are rarely called 'hip-hoppers')
Sorry for all that long information, I tried to explain it the best way. I hope I helped. Peace.