As I see it there are two versions of ‘shoving’ in 5e: a physical verion and a magical version.
The physical version allows pushing an opponent backwards OR knocking them prone, while the magic version moves them towards you or away from you but does not mention possibly knocking them prone.
The physical version is described on p. 195 (PHB) as follows,
"Using the Attack action, you can make a Special melee Attack to shove a creature, either to knock it prone or push it away from you. If you’re able to make multiple attacks with the Attack action, this Attack replaces one of them. The target must be no more than one size larger than you and must be within your reach. Instead of Making an Attack roll, you make a Strength (Athletics) check contested by the target’s Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). If you win the contest, you either knock the target prone or push it 5 feet away from you."
The Shield Master feat (p.170 of PHB) allows for this physical version as well.
The Telekinetic feat in Tashas C. of E. (p.81) is described this way,
"As a bonus action, you can try to telekinetically shove one creature you can see within 30 feet of you. When you do so, the target must succeed on a Strength saving throw (DC 8 + your proficiency bonus + the ability modifier of the score increased by this feat) or be moved 5 feet toward or away from you. A creature can willingly fail this save.
Certain spells and other magical abilities, such as thorn whip and the eldritch invocation Grasp of Hadar, move opponents closer to, or farther from the caster, but do not mention the possibility of knocking the opponent prone.
I can imagine a reasonable explanation for why/how there are two versions: the physical is a crashing, concussive impact, while the magical is perhaps more like a tractor beam or magnetic attraction or repulsion and–possibly–not as abrupt.
But if there are two versions, does that lead to further issues?
Perhaps it’s a separate question, but I ask here to highlight why/how answers to my initial question might matter:
Is the telekinetic (magic) version of a shove something that could reasonably be a surprise to an opponent–would/should that give some disadvantage on the opponent’s chance to resist being shoved?
If an opponent were magically shoved from behind, when they didn’t think anyone was there, would that be a reasonable basis for giving advantage to anyone attacking them from the front?
I’d appreciate any thoughtful input on this–whether directly answering the initial question or just focusing on other aspects. I want to understand how ‘shove’ can be used and haven’t seen much online that explores the topic. Of course each DM could rule as they see fit, and talking about this ahead of time to flesh out some aspects of the spell would be wise (I just emailed my DM to do so), but I’m glad for any input here, as well.