While in many parts of Spain the tapas bars or in the Basque Country/Navarra the pintxos bar don't all have seating, as the very longstanding local tradition is to enjoy your tapas or pintxos standing up, one ordering one tapa or pintxo and one drink per bar and then moving on to the next....the majority in the south do have seating, or at least limited seating. I do this regularly, both in the north, here in Madrid and in the south.

If you choose some Granada tapas bars, for example, the Los Diamantes local chain, especially the one on Plaza Nueva, you will find seating of some sort. And even at Bodegas Castañeda, one of the tapas bars featured in virtually all of the Spain travel guides, there is seating on the terrace.

And in Sevilla, all the tapas bars that I frequent regularly having seating, either at the bar, in the bar at high tables (as in Casa Morales or Azotea on Mateo Gagos or Casa Román on the Plaza de los Venerables or Bodeguita A. Romero in El Arenal, for 3 examples), or on the outdoor terrace.

In Córdoba, for example, there no seating at the bar at Casa el Pisto, but there is inside. One can come here simply for a dish of salmorejo or a mazamorra or another "tapa".
Ditto to Taberna la Montillana, where there is seating at the bar, and Bodegas Campos where there is ample table seating in the bar area or at the counter.
There are multiple examples of tapas taken seated in all southern Spain cities, whether it be Sevilla, Granada, Córdoba, Cádiz, etc.

As to enjoying tapas not in a tapas bar, that depends on the city and whether the particular restaurant serves tapas along side its regular restaurant menu.

In Sevilla many sit-down restaurants do serve tapas, such as Becerrita, enjoyed at the bar at high tables or counter chairs at the bar itself. Ditto to La Tienda de Azotea on Conde de Barajas. Tapas at the counter bar or at high tables, no problem. And on and on, Taberna Zurbarán, Salmedina, La Barra de Inchausti, etc.

In Granada, the Puerta del Carmen and the venerable Chiquito serve tapas at the bar or on the outdoor terrace, for example, although one can order larger dishes, restaurant style.