Why on iPhone only LTE and no 4g?

I have contract with O2 mobile internet 4g. On my old phone Huawei p20 pro I had 4g, later I bought iphone 11 per max and just changed the SIM card but I only get LTE on iPhone why? Have tried the SIM card from Vodafone because it gets 4g displayed.

LTE and 4G are both the same, only the child has a different name

And why about 4G Vodafone displayed?

No matter which provider, that comes from the manufacturer of the smartphone.

4G and LTE are the same no matter what is displayed.

4G equals LTE?
There are basically two answers to this question. One for everyday life and you as a user, as well as a technical.

Users: For you as a user, you can summarize briefly that LTE and 4G mean the same thing. Specifically, the fourth-generation mobile technology (hence 4G), which is also abbreviated to "LTE". LTE stands for "Long Term Evolution". The standard provides significantly higher data transfer rates, compared to its predecessors UMTS / HSDPA (up to 42 MBit). Today's 4G data networks theoretically support speeds of 300-500 MBit. In practice, transmission rates of 50-200 Mbps are more realistic even under ideal conditions - among other things because all users in the vicinity must share a radio cell and its capacity. More about this https://www.lte-anbieter.info/ratgeber/schnelligkeit-lte.php.

Technique: From a technical point of view, however, there's a small difference! According to the official standardization criteria, the first LTE generation in this country was not a "real 4G" yet. It should have been 3.9xG correctly. Only with the introduction of https://www.lte-anbieter.info/lte-advanced/ (from https://www.lte-anbieter.info/technik/kategorien-und-3gpp-release.php) experts really speak of 4G. By contrast, 4.5G (https://www.lte-anbieter.info/lte-advanced/pro.php) refers to a precursor to the LTE successor https://www.lte-anbieter.info/5g/, which has been upgraded since mid-2019 in Germany. The reason why both were linguistically blended, was purely in the marketing of mobile service providers located. For 4G was much easier to market than for example "3.95G". A similar development could be seen in the development towards 5G. Even when the mobile radio technology was not even standardized standardized, internationally some hardware manufacturers and network operators were already promoting "5G" - but rather meant a kind of "Pre 5G". This was of course similar nonsense, as at the LTE introduction

https://www.lte-anbieter.info/faq/4g-lte-das-selbe.php

Because you do not use Android device but n ios device, with me (samsung s9 plus) is synonymous never 4g or lte, then there's H or H + (HSPA HSPA +, so lte or lte in a little faster)

Wrong: not from the manufacturer of the smartphone, but from the network operator

OK, I did not know that. But there's also a difference between the manufacturers, or not? I know people with the same provider as me, where "LTE" is displayed (iOS), with me "4G" or "4G +" is displayed (Android).

That is new to me.
I know it as an iOS user only depending on the network. When I was still at Vodafone, I had 4G, now at Telekom it is LTE

we're probably both right and a mix of it is

The display is generated by the software and the SIM card setting. It can be either "4 G" or (Apple always "LTE" to be displayed.) There's no technical difference.