In the movies, Peter and Harley have never interacted with one another. They are both present at Tony Stark's funeral, but if they had shared words or glances it was never shown. They do have shared relations though.
Generally they are both perceived as 'Tony's Stark's Kids' along with Morgan. This is because Tony generally acted like a father to Peter while serving as a mentor, and because of how parental Tony was towards a young Harley in Iron Man 3.
This ship mostly stemmed from fandom speculation. Both boys are around the same age, are both geniuses, and are both proteges of Tony Stark. So it wasn't unlikely that once discovered they drew in quite a following.
There are several fanon things in this rare pair's fanbase that are considered true throughout most of their works. Probably the biggest thing is that Harley's unnamed sister mentioned in Iron Man 3 is named Abbie/Abby. Another one is that Harley and Tony never lost touch, and that they maintained a stable relationship throughout the course of the MCU. Another one is that Harley isn't a science genius (he is extremely smart in that field though just not a genius) but more of a mechanical one, as in he works with cars and physical devices rather than chemicals. Another one is that Harley takes on the mantle of 'Iron Lad' either while Tony is still alive or after his death.
Though there are roughly around 400 AO3 works for these two (and counting), there are some common story lines throughout their fics. One is that one of the two boys loathes the other before meeting them for taking up all of Tony's time or in fear that they are being replaced. This is often gets cleared up by the two actually meeting each other. Another one is the classic identity mix up with Harley falling for either Peter or Spider-Man and then hating the other. This is obviously all fixed with a simple identity reveal. Another common theme is at Tony's funeral. It often shows the two meeting and interacting there, finding comfort in one another. Lastly, there is the iconic Peter Parker's field trip to Stark Industries trope. This is not a Spiderlad exclusive trope, as it is so commonly found in thousands of other (commonly Irondad Gen) fics. But there are plenty of fics with a nice Spiderlad twist on them.
|SHIPS||het||BobbiFitz • Brutasha • Clintasha • FitzSimmons • Fosterson • Huntingbird • Iron Widow • JessLuke • Kitscliffe • MayWard • NebulaRhodey • PeggySous • Philinda • Romanogers • Scarlet America • Spider Witch • Static Quake • Steggy • Winter Widow • Thunderwar • YoYoMack|
|slash||Capsicoul • FitzHunter • FitzMack • FitzWard • Hawksilver • Iron Husbands • IronStrange • Iron Winter • JackDaniels • Roquill • SamBucky • SamSteve • Science Boyfriends • Spiderlad • Stackie • Stony • Stucky • T'Chalcon • Thunder Science • ThunderShield|
|femslash||Cartinelli • Danbeau • Scarlet Widow • Simmorse • Valcarol|
|non-binary||FrostHawk • FrostIron • Frostmaster • Lokane • Scarlet Vision • Valki|
|family||Domestic Avengers • Iron Dad|
|CHARACTERS||m/f||Bucky Barnes • Natasha Romanoff • Steve Rogers • Tony Stark|