Yes it is true buth there are some differences in them.
When you lust as a man, it is true that sex is Paramount because the main intention driving the list is sex. So the moment the man satisfy his lustful desire, he is okay and seems okay. In this situation, there is no love or should I say no true love in between the reason because lust does not always carries love but the urge to always have sex and sex is what is present in lust.
Now back to the second one, it is true that when you love, sex is still much more involved but the difference in it is that love controls the sex urge. That is why you will see some married couple that have not have sex for the past several months but they still love themselves. The love is still much more there, the love is still controlling the sex not the sex controlling the love.
I will say this are the little differences I can point out from the two questions you asked, I hoped it helps.
Well different individual have their own manner at which they view "love"...well some people believe that having sex with a person is a way to show love to that person while some people believe that true love does not demand sex before we can prove our love for a person....so different strokes for different folks...