100%. Its even personal preference on how they play. For example, the LP is a super heavy guitar, but you dont get that from just looking at pictures. They can weigh almost 10 pounds, because they are a solid chunk of mahogany. But even weight aside, they feel a lot different from say, a strat because the neck is a bit shorter so the string tension is a bit less. And then they also sound totally different since you have the 2 humbuckers in the LP vs the 3 single coils in the strat. So it also kind of depends what you want to play. Humbuckers are a lot hotter of a pickup than a single coil.
Definitely try out whatever you are thinking about.
Well I think its an old wives tale that heavier guitars have more sustain. I dont know if thats true or not, but my LP definitely has more sustain than my strat, but its not really a fair comp because its a Gibson LP and a Squier Strat. Its also worth noting that most modern LP's have holes drilled under the top to relieve some weight. But they are still called solid body guitars since they dont resonate like a hollowbody.
But a solid body will definitely change the sound vs a hollow or semi hollowbody. If you are in the same room as your amp it will be a lot harder to get as much gain out of a hollow or semi because the body of the guitar will resonant from the amp potentially causing feedback.
Of the two guitars you posted one was dual humbuckers and the other was HSH with a single coil in that middle position. I didnt look at what kind of switch it has, but it probably allows you to get some out of phase sounds which is what gives the strat its "quacky" sound.
Well the type of wood definitely makes a difference. But sometimes you will see people argue that heavier guitars sustain longer, even being made out of the same type of wood.
If you are looking for more information about guitars, these two guys are super knowledgeable.
Rick tends to focus on more music production and songwriting than guitar playing (has a few that go into gear though), but Rhett has a ton of videos about how to go about choosing a guitar and looking at different types of guitars.