I don't entirely agree with the other answers I see here. From my experience, as well as looking at quantization values offered in DAWs, a swing feel can be varied, sometimes based on genre but other times based on the style of the players and/or composer.
The concept of swinging is that the note value that is swung, in your example the 1/8 note, is pushed back, closer to the following beat, making the first 1/8 note longer and the second 1/8 note shorter. The exact placement of the second 1/8 note does not have a specific definition, as I mentioned above, and often wouldn't be easily written with standard notation, as the swung note may only be stated properly with a very small note value accompanied by dots, rests and/or ties. For example, someone could have a swing value where the second 1/8 lines up with the 19th 1/128 note of a given beat, while another player might have their swing value line up with the 11th 1/64 note of a given beat. Both players would be said to be swinging because their second 1/8 note is shorter than the first and closer to the following beat.
So generally speaking, swinging is just making the second of your notes shorter. This is often done with 1/16 notes in Jazz, possibly more commonly than 1/8 notes but I don't have any statistics to back that up. A note that is pushed further back is said to swing "harder".
There are some genres where a swung note is typically equivalent to a triplet value, like you provided in the question. For example, Rock and Pop music tend to use a triplet value for a swing feel. Swing has also appeared in traditional musics and Classical music, which is based on a triplet feel but is sometimes referred to as a "lilt". I have heard Jazz players suggest that a triplet feel for swing is "lame" or "amateur", typically preferring a heavier swing.
I would suggest listening to a variety of Jazz players playing at different tempos (as tempo can influence the desired swing value) and try to feel out the difference between their swing values (just keep in mind that they are very often swinging the 1/16 note, so the 1/8 note values will be even, not swung). If needed, slow the music down and subdivide the beat so that you can try to nail down the placement. Once you become more familiar with swing in general, you should be able to feel the difference more inherently.