Is the word ligar the same in Brazilian and European Portuguese?

No

The core meanings of the word remain the same in both variants: to turn on (an appliance), to connect (wires or ideas), and to call (on the phone). However, there is a difference in typical usage regarding the preposition required when referring to making a phone call or relating to something. In Brazil, the preposition para is the standard (ligar para alguém). In Portugal, the preposition a is very common and often considered the standard in many contexts (ligar a alguém).

Brazilian Portuguese Examples:

1. Eu vou ligar para você amanhã. (I will call you tomorrow.)
2. Você pode ligar o computador? (Can you turn on the computer?)
3. Ele ligou para o médico agora pouco. (He called the doctor a little while ago.)
4. Eu não ligo para o que ele diz. (I don't care about what he says.)
5. Você precisa ligar os cabos corretamente. (You need to connect the cables correctly.)

Continental Portuguese Examples:

1. Eu vou ligar-te amanhã. (I will call you tomorrow.)
2. Podes ligar o computador? (Can you turn on the computer?)
3. Ele ligou ao médico há pouco. (He called the doctor a little while ago.)
4. Eu não ligo ao que ele diz. (I don't care about what he says.)
5. É preciso ligar os cabos corretamente. (It is necessary to connect the cables correctly.)