One Factor vs. Two Factor ANOVA [One Way vs Two Way]

What is a factor in a Analysis of variance? A factor is, for example, the gender of a person with the characteristics male and female, the form of therapy used for a disease with therapy A, B and C or the field of study with, for example, medicine, business administration, psychology and math.
In the case of variance analysis, a factor is a categorical variable. You use an analysis of variance whenever you want to test whether these categories have an influence on the so-called dependent variable.
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[@catherinelee9723]

Is one way anova= one factor anova?
And two way anova= two factor anova?
Googling this for a long time but to no avail, appreciate your help

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Yes it is same thing

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[@yohanesb.1728]

dear prof,
I want to test whether public exposure (IV2) to norm violations and relations with perpetrators (IV 1) of norm violations have an effect on observer vicarious embarrassment (VE).
So there are two factors that cause VE, namely public exposure and relations with perpetrators of norm violations. Public exposure has two levels, namely (a) there is exposure and (b) there is no exposure/quiet. Level relationships: (a) Friends and (b) strangers. I'm planning to use a vignette to get the VE data. My question is:
1). Should the vignette show two directly interacting variables such as: "My friend (IV2) spoke loudly in the library and was seen by many people (IV1), how embarrassed are you for her actions?" or
2) vignette only contains information for each level independently. Examples in friendship relationships: My friend (IV1) spoke loudly in the library, how embarrassed are you for what he did?, Someone you don't know (IV1) spoke loudly in the library how embarrassed were you for what he did?
I think that to get the main effect, the simulation is carried out per level, and then a statistical test of the interaction between IV1 and IV2 is carried out.
Meanwhile, if the vignette contains two IVs that interact directly with each other, such as (friends x public exposure), (foreigners x public exposure), then this has directly tested the interaction effect so that the main effect for each IV is not obtained. Is my thinking correct?
The analysis is repeated measures for 4 different conditions.
thank you for your kindness.