Hip Hop is not a musical genre (although many people consider it to be so).
It is a cultural movement characterized by four elements, all of which represent the different manifestations of the culture: Rap music [oral] ; Turntablism or "DJing" [aural] ; B-boying [physical] ; Graffiti art [visual] .
So basically, when someone refers to Hip Hop this is encompassing the whole culture in which rap is just one of all elements.
musicfans.stackexchange.com/users/75/Renan Gomes
From my understanding Rap Music and Hip Hop music are the same, however Hip Hip music and Rapping are different.
Hip hop music :
Hip hop music, also called hip-hop, rap music, or hip-hop music, is a music genre consisting of a stylized rhythmic music that commonly accompanies rapping, a rhythmic and rhyming speech that is chanted.
Rapping: Rapping is often associated with and a primary ingredient of hip hop music, but the origins of the phenomenon can be said to predate hip hop culture by centuries.
So Rap would be a Speech and Hip Hop a Genre.
Also, Rap is more about the poetry of words and word styles and Hip Hop is more about the music(beats).
Additional Info:
What is the Difference between Rap and Hip Hop?
musicfans.stackexchange.com/users/99/Pobrecita
Rapping is a style of long-form narrative poetry recitation with a strong and regular rhythmic beat, typically spoken, but occasionally delivered in a sing-song fashion (Nelly, Bone-Thugs-N-Harmony).
Rap is most closely associated with the hip-hop musical genre, which often includes sampling, vinyl scratching, rapping, a distinctive beat, a deconstructionist aesthetic, and an urban sensibility.
Rap can be included in any genre, however, and has been featured in rock, heavy metal and country, among others.
(Many modern pop songs include a rapped verse or bridge as a way of adding a bit of "edge.")
Likewise, the hip-hop genre is not exclusively associated with rapping.
The music of singers such as Mary J. Blige and Frank Ocean is generally considered in the realm of hip-hop despite not always including rapping, and rappers such as Lauryn Hill and Wyclef Jean have occasionally released hip-hop songs that are sung, not rapped.
Both terms, and the linkage between the two, were popularized by the Sugarhill Gang's pioneering hip-hop rap song Rapper's Delight which featured the famous hook "I said a hip, hop, the hippie the hippie dibby
hip hop hop
and you don't stop to rock it to the bang bang boogie..."
musicfans.stackexchange.com/users/92/Chris Sunami supports Monica
To my understanding, rap music is usually all about the lyrics, while hip-hop can simply be a 'street' style of house beats or other genres.
musicfans.stackexchange.com/users/204/DJ Aftershock
Rap music is the combination of rhyming and poetry to a beat.
It is part of the Hip-Hop genre, which involves lyrics over fast-paced music.
Some people have described Hip-Hop as a way of life and a subculture, while rap is a specific genre of music.
The Grammys for the Hip-Hop category include R&B and Rap subcategories.
From Diffen .
musicfans.stackexchange.com/users/316/JMP
I think hip hop is more like an entertainment industry that is part of the history and culture of African civilization.
This includes Dances, Clothes, Music, Singing, and so on.
All this is summed up in one - Hip Hop Culture.
rap on the other hand is the voice of the street, the voice of the poor man who recruits to seek an opinion against someone or against the regime in which he lives, from here comes the rapping That is only main opinion.
Martin WC from Million Rap Views
musicfans.stackexchange.com/users/4747/Martin WC
What is the difference between 'hip hop' and 'rap' genres?
What is the difference between hip hop and rap?
musicfans.stackexchange.com
<hip-hop><rap>
musicfans.stackexchange.com/questions/65
musicfans.stackexchange.com/users/93/Avis
Hip hop music and rap music cover the same styles, but hip hop is broader and also encompasses a subculture and way of life. Hip Hop and Rap music are the same genre of music but rapping is different to Hip Hop music.Rap music focuses on the lyrics while Hip Hop music focuses on the sound and melody and while Hip Hop is a lifestyle,  Rap music is a specific genre. 
There is no difference between the two music genres but the act of rapping is different to Hip Hop music  The two genres have two different objectives. In Rap music more importance is given to the Lyrics whilst the melody is more important in Hip Hop music  Hip Hop is a lifestyle while Rap music is a specific genre 