Does it cost extra to text abroad if your on pay monthly?

Yes and No.

If you are the one that is abroad then yes, as you have to pay the cellphone company whose network that you are using. These types of charges can take up to 3 months after the fact to appear on your monthly bill.

If you are at home, and you have a friend who is abroad but bought their phone from the country that you are in, then you will not be charged extra for texting them as you use the same number as you usually, However, the person receiving the text may be charged.

If Both you and your friend are abroad, and both of your phones are from the same country, you will be charged for sending and your friend will be charged for receiving because even though you are on the same network in the country, your text will bounce from the country of origin, back to your home country and then back to where your friend is.

This answer is based on what happens if your home country is the UK.

Hope this helps.