The Lightroom catalog is a database that contains references to your images (drive+path+filename), the image metadata, and all your edits.
The original image files are never changed/edited.
To see your edits outside of Lightroom, you "export" the edits into new image files (JPG or TIF), which you can upload to websites.
Since the edits are nondestructive due to them being stored in the catalog, you can undo/redo/edit-somemore with no damage to the original files.
The main image organization is in folders on your hard drive.
Inside of LR, you can group images together in "collections", which can be nested. This would probably be similar to an "album".
Keywords can be added to your images, stored in the catalog. These keywords can be used for creating "collections" as well as searching.
Both Lr and iPhoto are what are called parametric image editors: they store references to the location of the files, and store parameters about how to adjust or edit the files, rather than changing the file itself. Sort of like giving someone instructions on how to develop a photo from a negative. They are both non-destructive; you don't "save" or "save as..."; the original isn't touched, and you don't see the result of your edits or adjustments till you export, sorta like one would after printing from a negative.
iPhoto takes it a step further, however, and can create a managed library. By default it COPIES all your images to a library, which is nothing but a special folder called a "package" that limits access. It still references the photos in there, and they are there in folders (peek inside with the command "show package contents"). Lr does NOT do that; it only references images, it doesn't put them in a hidden library. They are out there, and accessible at all times in the Finder. With iPhoto, and a managed library, you cannot see the masters that are in the managed library.
Lr will let you edit and export to a folder for uploading, just like in iPhoto.
Lr will let you edit in an external editor, like PSE, although you may find it easier in Lr.
Lr will import to a folder, which is the same as a folder out in the Mac Finder, like ~/Pictures/2016-01-10 or whatever. It's the same as the Finder folder. Lr can either copy a photo to there (or a different folder, or create one), or move it there, or add it (if, eg, it was already in the folder "2016-01-01").
Lr then has virtual containers that are the functional equivalent of albums in iPhoto, called collections and collection sets. Like albums, one photo can be in many different albums. Lr does not do "events" per se, however. An event is really just a smart album for a date, and Lr can do those.
The file names won't change unless you want 'em to, manually or in a batch or via a plugin or some other way. They can be changed on export, or when published online and so on. All the metadata is there.
One big difference over iPhoto is that you have MUCH more control over that metadata. You can add tons of info, copy it, batch process it, etc. And unlike iPhoto, you can save that metadata right to the images within Lr. So if you add keywords, they can get written right to the image. So you can search for keywords right in Spotlight, or captions or people.
One downside of Lr is that it's harder to look "inside" Lr from other Mac applications to find photos. Apple applications like Mail have a media browser that can see edited photos and albums and whatnot within iPhoto's library; it's rare to have that same access into Lr's catalog. OTOH, since the images Lr references are right there in the Finder folders, they are easier to find in other situations, just as you'd find any file in a Mac folder.
Best thing is to download the demo, and start with a small group of photos and play around with it. You''ll get used to it pretty quickly.
I use a Mac, currently use iPhoto as the storage place for my photos. I have them in albums, and resize to a certain shape then export at a certain size to a folder on the desktop, then upload this folder to a website. If I need to edit any of them, I edit the original full size jpeg in Photoshop Elements 9 which has done everything i have needed to do. It has worked well doing this for years. Now I am looking at changing to Lightroom, does this work in the same or similar way, i.e can i import to an album or event, crop and export as they are to a desktop folder, then upload elsewhere.........leaving any editing for later. I need to retain all file info, e.g. photo number , and metadata so I can find image ABCD1234 if I have to!
Any help much appreciated as its getting confusing when first reading the "how to" manual after so many years using iPhoto.
Although both the above answers are correct your main question does "Lightroom work the same or similar as iPhoto" and the answer to that question is yes it does, in certain ways, and no it doesn't, in other ways.
The Top No it doesn't is because iPhoto stores your images inside of a Package. A type of folder where the contents of that folder are hidden from the user making it somewhat hard for the User to actually get to their Real original images. iPhoto want to Control how you access the original images.
Lightroom does not move or copy your images into its own folder structure and does not restrict the original images from you accessing them outside of LR like from a File Manager like Finder.
You create folders, or tell LR to create folders during import, where your images are stored. That can be any place on your computers internal hard drive, an external drive or a networked drive.
No you don't import to any Albums or Event. LR doesn't do Albums or Events but it does have Collections where you can group images for Display (That is Display inside LR) and you can create a Collection at the time of import.
Yes LR has the option to Send images to an External editor of your choice. I am sure it will work with Adobe Photoshop Elements 9.
LR is a much more powerful program than iPhoto.
I suggest you start by viewing some of the many online tutorials on how LR works and how to work with LR. Taking the time to do that will save you a lot of time and headaches when and if you switch over to LR.
Thankyou......that makes it easier.